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Artigos de revistas sobre o tema "Complex foliations"

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Autor: Grafiati

Publicado: 7 de julho de 2024

Última modificação: 7 de julho de 2024

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1

Deroin, Bertrand, e Adolfo Guillot. "Foliated affine and projective structures". Compositio Mathematica 159, n.º 6 (15 de maio de 2023): 1153–87. http://dx.doi.org/10.1112/s0010437x2300711x.

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We formalize the concepts of holomorphic affine and projective structures along the leaves of holomorphic foliations by curves on complex manifolds. We show that many foliations admit such structures, we provide local normal forms for them at singular points of the foliation, and we prove some index formulae in the case where the ambient manifold is compact. As a consequence of these, we establish that a regular foliation of general type on a compact algebraic manifold of even dimension does not admit a foliated projective structure. Finally, we classify foliated affine and projective structures along regular foliations on compact complex surfaces.

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2

Mol, Rogério S. "Flags of holomorphic foliations". Anais da Academia Brasileira de Ciências 83, n.º 3 (29 de julho de 2011): 775–86. http://dx.doi.org/10.1590/s0001-37652011005000025.

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A flag of holomorphic foliations on a complex manifold M is an object consisting of a finite number of singular holomorphic foliations on M of growing dimensions such that the tangent sheaf of a fixed foliation is a subsheaf of the tangent sheaf of any of the foliations of higher dimension. We study some basic properties oft hese objects and, in <img src="/img/revistas/aabc/2011nahead/aop2411pcn.jpg" align="absmiddle" />, n > 3, we establish some necessary conditions for a foliation, we find bounds of lower dimension to leave invariant foliations of codimension one. Finally, still in <img src="/img/revistas/aabc/2011nahead/aop2411pcn.jpg" align="absmiddle" /> involving the degrees of polar classes of foliations in a flag.

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3

AZEVEDO SCÁRDUA, B. C., e J. C. CANILLE MARTINS. "ON THE GROWTH OF HOLOMORPHIC PROJECTIVE FOLIATIONS". International Journal of Mathematics 13, n.º 07 (setembro de 2002): 695–726. http://dx.doi.org/10.1142/s0129167x02001502.

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In the theory of real (non-singular) foliations, the study of the growth of the leaves has proved to be useful in the comprehension of the global dynamics as the existence of compact leaves and exceptional minimal sets. In this paper we are interested in the complex version of some of these basic results. A natural question is the following: What can be said of a codimension one (possibly singular) holomorphic foliation on a compact hermitian manifold M exhibiting subexponential growth for the leaves? One of the first examples comes when we consider the Fubini–Study metric on [Formula: see text] and dimension one foliations. In this case, under some non-degeneracy hypothesis on the singularities, we may classify the foliation as a linear logarithmic foliation. In particular, the limit set of ℱ is a union of singularities and invariant algebraic curves. Applications of this and other results we prove are given to the general problem of uniformization of the leaves of projective foliations.

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4

Martelo, Mitchael, e Bruno Scárdua. "On groups of formal diffeomorphisms of several complex variables". Anais da Academia Brasileira de Ciências 84, n.º 4 (dezembro de 2012): 873–80. http://dx.doi.org/10.1590/s0001-37652012000400002.

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In this note we announce some results in the study of groups of formal or germs of analytic diffeomorphisms in several complex variables. Such groups are related to the study of the transverse structure and dynamics of Holomorphic foliations, via the holonomy group notion of a foliation's leaf. For dimension one, there is a well-established dictionary relating analytic/formal classification of the group, with its algebraic properties (finiteness, commutativity, solvability, among others). Such system of equivalences also characterizes the existence of suitable integrating factors, i.e., invariant vector fields and one-forms associated to the group. Our aim is to state the basic lines of such dictionary for the case of several complex variables groups. Our results are applicable in the construction of suitable integrating factors for holomorphic foliations with singularities. We believe they are a starting point in the study of the connection between Liouvillian integration and transverse structures of holomorphic foliations with singularities in the case of arbitrary codimension. The results in this note are derived from the PhD thesis "Grupos de germes de difeomorfismos complexos em várias variáveis e formas diferenciais" of the first named author (Martelo 2010).

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5

Scardua, Bruno Cesar Azevedo, e Liliana Jurado. "On transversely holomorphic foliations with homogeneous transverse structure". Proceedings of the International Geometry Center 16, n.º 3 (12 de novembro de 2023): 192–216. http://dx.doi.org/10.15673/pigc.v16i3.2304.

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In this paper we study transversely holomorphic foliations of complex codimension one with a transversely homogeneous complex transverse structure. We prove that the only cases are the transversely additive, affine and projective cases. We shall focus on the transversely affine case and describe the holonomy of a leaf which is "at the infinity" with respect to this structure and prove this is a solvable group. Using this we are able to prove linearization results for the foliation under the assumption of existence of some hyperbolic map in the holonomy group. Such foliations will then be given by simple-poles closed transversely meromorphic one-forms.

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6

Tomassini, Giuseppe. "Foliations with complex leaves". Banach Center Publications 31, n.º 1 (1995): 367–72. http://dx.doi.org/10.4064/-31-1-367-372.

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7

Araujo, Carolina, e Paulo João Figueredo. "Foliations on Complex Manifolds". Notices of the American Mathematical Society 69, n.º 07 (1 de agosto de 2022): 1. http://dx.doi.org/10.1090/noti2507.

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8

Ida, Cristian. "On complex Riemannian foliations". Journal of Physics: Conference Series 670 (25 de janeiro de 2016): 012025. http://dx.doi.org/10.1088/1742-6596/670/1/012025.

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9

Gigante, Giuliana, e Giuseppe Tomassini. "Foliations with complex leaves". Differential Geometry and its Applications 5, n.º 1 (março de 1995): 33–49. http://dx.doi.org/10.1016/0926-2245(95)00004-n.

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10

González-Dávila, José Carmelo. "Harmonicity and minimality of complex and quaternionic radial foliations". Forum Mathematicum 30, n.º 3 (1 de maio de 2018): 785–98. http://dx.doi.org/10.1515/forum-2017-0076.

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AbstractWe construct special classes of totally geodesic almost regular foliations, namely, complex radial foliations in Hermitian manifolds and quaternionic radial foliations in quaternionic Kähler manifolds, and we give criteria for their harmonicity and minimality. Then examples of these foliations on complex and quaternionic space forms, which are harmonic and minimal, are presented.

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11

Suhr, Günter, Tom Calon e Sherry M. Dunsworth. "Origin of complex upper mantle structures in the southern Lewis Hills (Bay of Islands Ophiolite, Newfoundland)". Canadian Journal of Earth Sciences 28, n.º 5 (1 de maio de 1991): 774–87. http://dx.doi.org/10.1139/e91-067.

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The Springers Hill area (Lewis Hills, Bay of Islands Ophiolite) may represent oceanic lithosphere created in close proximity to the nontransform segment of an oceanic fracture zone. Upper mantle rocks exposed on Springers Hill were investigated to establish whether their development was affected by the thermal and rheological changes associated with oceanic fracture zones. Harzburgites of the Springers Hill area reveal complex structural patterns. On a small scale, foliations defined by orthopyroxene grains intersect foliations defined by spinel grains at various angles. Olivine petrofabric work demonstrates that only the spinel foliation is related to the preserved flow plane. The orthopyroxene foliation appears to be the result of pull-apart of formerly larger grains during high-temperature deformation. On the larger scale, orientation patterns of foliation, lineation, and dykes suggest that strike-slip movement occurred parallel and at high angle to the fracture- zone contact at various stages of a complex flow history. Given its location adjacent to a nontransform segment of oceanic lithosphere, the origin of the strike-slip movement parallel to the fracture zone must be clarified. It can be accounted for by movement of the older lithosphere past asthenosphere of the young spreading ridge during plate-driven flow.

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12

León, Victor, Mitchael Martelo e Bruno Scárdua. "Irreducible holonomy groups and first integrals for holomorphic foliations". Forum Mathematicum 32, n.º 3 (1 de maio de 2020): 783–94. http://dx.doi.org/10.1515/forum-2019-0129.

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AbstractWe study groups of germs of complex diffeomorphisms having a property called irreducibility. The notion is motivated by the similar property of the fundamental group of the complement of an irreducible hypersurface in the complex projective space. Natural examples of such groups of germ maps are given by holonomy groups and monodromy groups of integrable systems (foliations) under certain conditions. We prove some finiteness results for these groups extending previous results in [D. Cerveau and F. Loray, Un théorème de Frobenius singulier via l’arithmétique élémentaire, J. Number Theory 68 1998, 2, 217–228]. Applications are given to the framework of germs of holomorphic foliations. We prove the existence of first integrals under certain irreducibility or more general conditions on the tangent cone of the foliation after a punctual blow-up.

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13

CÂMARA, LEONARDO M., e BRUNO A. SCÁRDUA. "Periodic complex map germs and foliations". Anais da Academia Brasileira de Ciências 89, n.º 4 (dezembro de 2017): 2563–79. http://dx.doi.org/10.1590/0001-3765201720170233.

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14

Saeki, Akihiro. "On foliations on complex spaces, II". Proceedings of the Japan Academy, Series A, Mathematical Sciences 69, n.º 1 (1993): 5–9. http://dx.doi.org/10.3792/pjaa.69.5.

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15

Jelonek, Włodzimierz. "Complex foliations and Kähler QCH surfaces". Colloquium Mathematicum 156, n.º 2 (2019): 229–42. http://dx.doi.org/10.4064/cm7244-4-2018.

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16

Brunella, Marco. "Codimension one foliations on complex tori". Annales de la faculté des sciences de Toulouse Mathématiques 19, n.º 2 (2010): 405–18. http://dx.doi.org/10.5802/afst.1248.

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17

BALLICO, Edoardo. "Positive Foliations on Compact Complex Manifolds". Tokyo Journal of Mathematics 26, n.º 1 (junho de 2003): 15–21. http://dx.doi.org/10.3836/tjm/1244208680.

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18

Brunella, M. "Nonuniformisable Foliations on Compact Complex Surfaces". Moscow Mathematical Journal 9, n.º 4 (2009): 729–48. http://dx.doi.org/10.17323/1609-4514-2009-9-4-729-748.

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19

Chiossi, Simon G., e Paul-Andi Nagy. "Complex homothetic foliations on Kähler manifolds". Bulletin of the London Mathematical Society 44, n.º 1 (13 de setembro de 2011): 113–24. http://dx.doi.org/10.1112/blms/bdr074.

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20

Domínguez-Vázquez, Miguel. "Isoparametric foliations on complex projective spaces". Transactions of the American Mathematical Society 368, n.º 2 (23 de setembro de 2014): 1211–49. http://dx.doi.org/10.1090/s0002-9947-2014-06415-5.

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21

Lins Neto, A. "Germs of complex two dimensional foliations". Bulletin of the Brazilian Mathematical Society, New Series 46, n.º 4 (dezembro de 2015): 645–80. http://dx.doi.org/10.1007/s00574-015-0107-9.

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22

Bailey, Michael. "Symplectic Foliations and Generalized Complex Structures". Canadian Journal of Mathematics 66, n.º 1 (fevereiro de 2014): 31–56. http://dx.doi.org/10.4153/cjm-2013-007-6.

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AbstractWe answer the natural question: when is a transversely holomorphic symplectic foliation induced by a generalized complex structure? The leafwise symplectic form and transverse complex structure determine an obstruction class in a certain cohomology, which vanishes if and only if our question has an affirmative answer. We first study a component of this obstruction, which gives the condition that the leafwise cohomology class of the symplectic form must be transversely pluriharmonic. As a consequence, under certain topological hypotheses, we infer that we actually have a symplectic fibre bundle over a complex base. We then show how to compute the full obstruction via a spectral sequence. We give various concrete necessary and sufficient conditions for the vanishing of the obstruction. Throughout, we give examples to test the sharpness of these conditions, including a symplectic fibre bundle over a complex base that does not come from a generalized complex structure, and a regular generalized complex structure that is very unlike a symplectic fibre bundle, i.e., for which nearby leaves are not symplectomorphic.

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23

Andrada, Adrián. "Complex Product Structures and Affine Foliations". Annals of Global Analysis and Geometry 27, n.º 4 (junho de 2005): 377–405. http://dx.doi.org/10.1007/s10455-005-3897-y.

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24

Duchamp, T., e M. Kalka. "The equivalence problem for complex foliations of complex surfaces". Illinois Journal of Mathematics 34, n.º 1 (março de 1990): 59–77. http://dx.doi.org/10.1215/ijm/1255988492.

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25

Ohsawa, Takeo. "A Reduction Theorem for Stable sets of Holomorphic Foliations on Complex Tori". Nagoya Mathematical Journal 195 (2009): 41–56. http://dx.doi.org/10.1017/s0027763000009697.

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AbstractSome complex n-tori admit holomorphic foliations of codimension one besides the flat ones. It will be shown that such nonlinear foliations, possibly with singularities, can be reduced to those on 2-tori under some topological conditions. A crucial step is an application of the Hodge theory on pseudoconvex manifolds.

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26

Gotoh, Tohru. "Harmonic foliations on a complex projective space". Tsukuba Journal of Mathematics 14, n.º 1 (junho de 1990): 99–106. http://dx.doi.org/10.21099/tkbjm/1496161322.

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27

Santos, Fabio, e Bruno Scardua. "Stability of complex foliations transverse to fibrations". Proceedings of the American Mathematical Society 140, n.º 9 (1 de setembro de 2012): 3083–90. http://dx.doi.org/10.1090/s0002-9939-2011-11136-5.

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28

Tomassini, Giuseppe, e Sergio Venturini. "Contact geometry of one-dimensional complex foliations". Indiana University Mathematics Journal 60, n.º 2 (2011): 661–76. http://dx.doi.org/10.1512/iumj.2011.60.4202.

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29

Azevedo Scárdua, B. "Complex projective foliations having sub-exponential growth". Indagationes Mathematicae 12, n.º 3 (2001): 293–302. http://dx.doi.org/10.1016/s0019-3577(01)80011-2.

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30

Asuke, Taro. "Complexification of foliations and complex secondary classes". Bulletin of the Brazilian Mathematical Society 34, n.º 2 (1 de julho de 2003): 251–62. http://dx.doi.org/10.1007/s00574-003-0011-6.

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31

Scárdua, Bruno. "On Complex Codimension-One Foliations Transverse Fibrations". Journal of Dynamical and Control Systems 11, n.º 4 (outubro de 2005): 575–603. http://dx.doi.org/10.1007/s10883-005-8819-6.

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32

Berndt, Jürgen, e José Carlos Díaz-Ramos. "Homogeneous polar foliations of complex hyperbolic spaces". Communications in Analysis and Geometry 20, n.º 3 (2012): 435–54. http://dx.doi.org/10.4310/cag.2012.v20.n3.a1.

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33

Murphy, Thomas, e Paul-Andi Nagy. "Complex Riemannian foliations of open Kähler manifolds". Transactions of the American Mathematical Society 371, n.º 7 (23 de agosto de 2018): 4895–910. http://dx.doi.org/10.1090/tran/7492.

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34

Ballico, Edoardo. "Meromorphic singular foliations on complex projective surfaces". Annals of Global Analysis and Geometry 14, n.º 3 (agosto de 1996): 257–61. http://dx.doi.org/10.1007/bf00054473.

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35

SOARES, MARCIO G. "HOLOMORPHIC FOLIATIONS AND CHARACTERISTIC NUMBERS". Communications in Contemporary Mathematics 07, n.º 05 (outubro de 2005): 583–96. http://dx.doi.org/10.1142/s021919970500188x.

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We relate the characteristic numbers of the normal sheaf of a k-dimensional holomorphic foliation [Formula: see text] of a compact complex manifold Mn, to the characteristic numbers of the normal sheaf of a one-dimensional holomorphic foliation associated to [Formula: see text]. In case M is a complex projective space, we also obtain bounds for the degrees of the components of codimension k - 1 of the singular set of [Formula: see text].

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36

LORAY, FRANK, e JORGE VITÓRIO PEREIRA. "TRANSVERSELY PROJECTIVE FOLIATIONS ON SURFACES: EXISTENCE OF MINIMAL FORM AND PRESCRIPTION OF MONODROMY". International Journal of Mathematics 18, n.º 06 (julho de 2007): 723–47. http://dx.doi.org/10.1142/s0129167x07004278.

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We introduce a notion of minimal form for transversely projective structures of singular foliations on complex manifolds. Our first main result says that this minimal form exists and is unique when ambient space is two-dimensional. From this result, one obtains a natural way to produce invariants for transversely projective foliations on surfaces. Our second main result says that on projective surfaces one can construct singular transversely projective foliations with prescribed monodromy.

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37

NGUYÊN, VIÊT-ANH. "Directed harmonic currents near hyperbolic singularities". Ergodic Theory and Dynamical Systems 38, n.º 8 (2 de maio de 2017): 3170–87. http://dx.doi.org/10.1017/etds.2017.2.

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Let $\mathscr{F}$ be a holomorphic foliation by curves defined in a neighborhood of $0$ in $\mathbb{C}^{2}$ having $0$ as a hyperbolic singularity. Let $T$ be a harmonic current directed by $\mathscr{F}$ which does not give mass to any of the two separatrices. We show that the Lelong number of $T$ at $0$ vanishes. Then we apply this local result to investigate the global mass distribution for directed harmonic currents on singular holomorphic foliations living on compact complex surfaces. Finally, we apply this global result to study the recurrence phenomenon of a generic leaf.

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38

Auréjac, Jean-Baptiste, Gérard Gleizes, Hervé Diot e Jean-Luc Bouchez. "The Quérigut Complex (Pyrenees, France) revisited by the AMS technique : a syntectonic pluton of the Variscan dextral transpression". Bulletin de la Société Géologique de France 175, n.º 2 (1 de março de 2004): 157–74. http://dx.doi.org/10.2113/175.2.157.

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Abstract The Variscan Querigut Pluton (eastern Axial Zone, Pyrenees), recently dated at 307 ± 2 Ma, is a classical example for the structural study of granitoids. We present a new structural analysis of this pluton using the powerful technique of magnetic susceptibility anisotropy (AMS). A model of pluton emplacement is proposed on the basis of complementary microstructural analyses allowing the determination of the temperatures of fabric acquisition in the magmatic units, and of the shear sense criteria in the surrounding country rocks. This pluton is constituted by two main units that have intruded metasedimentary rocks where regional metamorphic conditions decrease from southwest to northeast. A well-foliated southern granodioritic unit, rich in Devonian marble xenoliths, is bounded to the south by Cambro-Ordovician metapelites. A weakly foliated northern monzogranitic unit, bounded to the north by Devonian marbles, comprises two sub-types : an outer biotite-monzogranite and an inner biotite-muscovite leucomonzogranite. Abundant basic stocks of variable sizes and lithologies outcrop in the granodioritic unit and in the southern part of the monzogranitic unit. Mean magnetic susceptibility and magnetic foliation maps show a very good agreement with the previous compiled petrographic and structural maps, strengthening the validity of the AMS technique. The northern monzogranitic units display two unevenly distributed structural patterns : (a) a NE-SW-trending pattern of weakly to steeply dipping foliations, dominant in the outer biotite monzogranite, is associated to subhorizontal NE-SW lineations ; and (b) a NW-SE-trending pattern of steeply dipping foliations, dominant in the inner biotite-muscovite monzogranite, is concentrated in NW-SE elongated corridors, associated to subhorizontal NW-SE lineations. In the southern granodioritic unit, foliation patterns follow roughly both the main regional foliation pattern and the pluton boundary, with foliation dips increasing to the south. Subhorizontal NW-SE trending magnetic lineations in the inner parts of this unit, are progressively verticalized toward the southern pluton boundary. A progressive increase in total magnetic anisotropy is observed toward the border of the pluton, correlated with both an increase in solid-state deformation and a decrease of the final temperature of fabric acquisition. These features result from a pluri-kilometric shear zone localized in the western half of the granodioritic unit, decreasing in thickness in its eastern half and along N060oE trending contacts with the country rocks. In the northern monzogranitic unit, one can roughly correlate the magmatic microstructures to the NE-SW trending fabric, and the superimposed subsolidus microstructures to the NW-SE-trending corridors, where rather low-temperature (< 300 oC) fluid-assisted cataclastic microstructures may also appear. The country-rocks, half kilometer away from the pluton border, display the D2 regional Variscan pattern, with subvertical and N110oE-striking foliations and subhorizontal and E-W-trending stretching lineations associated to a dextral shear. Closer to the pluton, the country-rocks are subjected to the pluton influence, particularly along the southern border where a strong flattening is associated to subvertical lineations related to local thrusting of the pluton onto its country rocks. An emplacement model is proposed through the injection of three principal magma batches (granodiorite, biotite-monzogranite and biotite-muscovite monzogranite) that successively and progressively built up the pluton while the whole region was subjected to a dextral and compressive deformation regime, in agreement with AMS results obtained from several other plutons of the Pyrenees.

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39

Campana, Frédéric. "Algebraicity of foliations on complex projective manifolds, applications". Mathematical Biosciences and Engineering 30, n.º 4 (2022): 1187–208. http://dx.doi.org/10.3934/era.2022063.

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<abstract><p>This is an expository text, originally intended for the ANR 'Hodgefun' workshop, twice reported, organised at Florence, villa Finaly, by B. Klingler. We show that holomorphic foliations on complex projective manifolds have algebraic leaves under a certain positivity property: the 'non pseudoeffectivity' of their duals. This permits to construct certain rational fibrations with fibres either rationally connected, or with trivial canonical bundle, of central importance in birational geometry. A considerable extension of the range of applicability is due to the fact that this positivity is preserved by the tensor powers of the tangent bundle. The results presented here are extracted from <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>, which is inspired by the former results <sup>[<xref ref-type="bibr" rid="b2">2</xref>,<xref ref-type="bibr" rid="b3">3</xref>,<xref ref-type="bibr" rid="b4">4</xref>]</sup>. In order to make things as simple as possible, we present here only the projective versions of these results, although most of them can be easily extended to the logarithmic or 'orbifold' context.</p></abstract>

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40

Shcherbakov, A. A. "Almost complex structures on universal coverings of foliations". Transactions of the Moscow Mathematical Society 76 (17 de novembro de 2015): 137–79. http://dx.doi.org/10.1090/mosc/250.

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41

Azevedo Scárdua, B. "Holomorphic Anosov systems, foliations and fibring complex manifolds". Dynamical Systems 18, n.º 4 (dezembro de 2003): 365–89. http://dx.doi.org/10.1080/14689360310001613620.

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42

Camacho, C., A. Lins Neto e P. Sad. "Minimal sets of foliations on complex projective spaces". Publications mathématiques de l'IHÉS 68, n.º 1 (janeiro de 1988): 187–203. http://dx.doi.org/10.1007/bf02698548.

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43

Kruglikov, Boris. "Symmetries of almost complex structures and pseudoholomorphic foliations". International Journal of Mathematics 25, n.º 08 (julho de 2014): 1450079. http://dx.doi.org/10.1142/s0129167x14500797.

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Contrary to complex structures, a generic almost complex structure J has no local symmetries. We give a criterion for finite-dimensionality of the pseudogroup G of local symmetries for a given almost complex structure J. It will be indicated that a large symmetry pseudogroup (infinite-dimensional) is a signature of some integrable structure, like a pseudoholomorphic foliation. We classify the sub-maximal (from the viewpoint of the size of G) symmetric structures J. Almost complex structures in dimensions 4 and 6 are discussed in greater details in this paper.

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44

Patrizio, G., e A. Spiro. "Foliations by stationary disks of almost complex domains". Bulletin des Sciences Mathématiques 134, n.º 3 (abril de 2010): 215–34. http://dx.doi.org/10.1016/j.bulsci.2009.06.004.

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45

Della Sala, Giuseppe. "Liouville-type theorems for foliations with complex leaves". Annales de l’institut Fourier 60, n.º 2 (2010): 711–25. http://dx.doi.org/10.5802/aif.2537.

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CAMACHO, CÉSAR, e RUDY ROSAS. "Invariant sets near singularities of holomorphic foliations". Ergodic Theory and Dynamical Systems 36, n.º 8 (21 de julho de 2015): 2408–18. http://dx.doi.org/10.1017/etds.2015.23.

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Resumo:

Consider a complex one-dimensional foliation on a complex surface near a singularity $p$. If ${\mathcal{I}}$ is a closed invariant set containing the singularity $p$, then ${\mathcal{I}}$ contains either a separatrix at $p$ or an invariant real three-dimensional manifold singular at $p$.

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Gudmundsson, Sigmundur. "Holomorphic harmonic morphisms from four-dimensional non-Einstein manifolds". International Journal of Mathematics 26, n.º 01 (janeiro de 2015): 1550006. http://dx.doi.org/10.1142/s0129167x15500068.

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Resumo:

We construct four-dimensional Riemannian Lie groups carrying left-invariant conformal foliations with minimal leaves of codimension 2. We show that these foliations are holomorphic with respect to an (integrable) Hermitian structure which is not Kähler. We then prove that the Riemannian Lie groups constructed are not Einstein manifolds. This answers an important open question in the theory of complex-valued harmonic morphisms from Riemannian 4-manifolds.

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Gotoh, Tohru. "A remark on foliations on a complex projective space with complex leaves". Tsukuba Journal of Mathematics 16, n.º 1 (junho de 1992): 169–72. http://dx.doi.org/10.21099/tkbjm/1496161837.

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Berndtsson, Bo, Dario Cordero-Erausquin, Bo'az Klartag e Yanir Rubinstein. "Complex interpolation of $\mathbb R$-norms, duality and foliations". Journal of the European Mathematical Society 22, n.º 2 (29 de outubro de 2019): 477–505. http://dx.doi.org/10.4171/jems/927.

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Kubo, Akira. "Geometry of homogeneous polar foliations of complex hyperbolic spaces". Hiroshima Mathematical Journal 45, n.º 1 (março de 2015): 109–23. http://dx.doi.org/10.32917/hmj/1428365055.

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