Relevant bibliographies by topics / Holomorphic immersion

Academic literature on the topic 'Holomorphic immersion'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Holomorphic immersion"

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Nomizu, Katsumi, Ulrich Pinkall, and Fabio Podestà. "On the geometry of affine Kähler immersions." Nagoya Mathematical Journal 120 (December 1990): 205–22. http://dx.doi.org/10.1017/s0027763000003342.

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In this paper we extend the work on affine immersions [N-Pi]-1 to the case of affine immersions between complex manifolds and lay the foundation for the geometry of affine Kähler immersions. The notion of affine Kähler immersion extends that of a holomorphic and isometric immersion between Kähler manifolds and can be contrasted to the notion of holomorphic affine immersion which has been established in the work of Dillen, Vrancken and Verstraelen [D-V-V] and that of Abe [A].
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Nomizu, Katsumi, and Fabio Podestà. "On the Cartan-Norden theorem for affine Kähler immersions." Nagoya Mathematical Journal 121 (March 1991): 127–35. http://dx.doi.org/10.1017/s002776300000341x.

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In [N-Pi-Po] the notion of affine Kähler immersion for complex manifolds has been introduced: if Mn is an n-dimensional complex manifold and f: Mn -→ Cn+1 is a holomorphic immersion together with an anti-holomorphic transversal vector field ζ, we can induce a connection ▽ on Mn which is Kähler-like, that is, its curvature tensor R satisfies R(Z, W) = 0 as long as Z, W are (1, 0) complex vector fields on M.
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Alghanemi, Azeb, Noura Al-houiti, Bang-Yen Chen, and Siraj Uddin. "Existence and uniqueness theorems for pointwise slant immersions in complex space forms." Filomat 35, no. 9 (2021): 3127–38. http://dx.doi.org/10.2298/fil2109127a.

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An isometric immersion f : Mn ? ?Mm from an n-dimensional Riemannian manifold Mn into an almost Hermitian manifold ?Mm of complex dimension m is called pointwise slant if its Wirtinger angles define a function defined on Mn. In this paper we establish the Existence and Uniqueness Theorems for pointwise slant immersions of Riemannian manifolds Mn into a complex space form ?Mn(c) of constant holomorphic sectional curvature c, which extend the Existence and Uniqueness Theorems for slant immersions proved by B.-Y. Chen and L. Vrancken in 1997.
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Alarcón, Antonio, and Franc Forstnerič. "Every conformal minimal surface in ℝ3 is isotopic to the real part of a holomorphic\break null curve." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 740 (July 1, 2018): 77–109. http://dx.doi.org/10.1515/crelle-2015-0069.

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Abstract We show that for every conformal minimal immersion {u:M\to\mathbb{R}^{3}} from an open Riemann surface M to {\mathbb{R}^{3}} there exists a smooth isotopy {u_{t}:M\to\mathbb{R}^{3}} ( {t\in[0,1]} ) of conformal minimal immersions, with {u_{0}=u} , such that {u_{1}} is the real part of a holomorphic null curve {M\to\mathbb{C}^{3}} (i.e. {u_{1}} has vanishing flux). If furthermore u is nonflat, then {u_{1}} can be chosen to have any prescribed flux and to be complete.
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Chen, Jingyi, and Ailana Fraser. "Holomorphic Variations of Minimal Disks with Boundary on a Lagrangian Surface." Canadian Journal of Mathematics 62, no. 6 (December 14, 2010): 1264–75. http://dx.doi.org/10.4153/cjm-2010-068-1.

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AbstractLet L be an oriented Lagrangian submanifold in an n-dimensional Kähler manifold M. Let u: D → M be a minimal immersion from a disk D with u(𝜕D) ⊂ L such that u(D) meets L orthogonally along u(𝜕D). Then the real dimension of the space of admissible holomorphic variations is at least n + μ(E, F), where μ(E, F) is a boundary Maslov index; the minimal disk is holomorphic if there exist n admissible holomorphic variations that are linearly independent over ℝ at some point p ∈ 𝜕D; if M = ℂPn and u intersects L positively, then u is holomorphic if it is stable, and its Morse index is at least n + μ(E, F) if u is unstable.
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EKHOLM, TOBIAS, JOHN ETNYRE, and MICHAEL SULLIVAN. "ORIENTATIONS IN LEGENDRIAN CONTACT HOMOLOGY AND EXACT LAGRANGIAN IMMERSIONS." International Journal of Mathematics 16, no. 05 (May 2005): 453–532. http://dx.doi.org/10.1142/s0129167x05002941.

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We show how to orient moduli spaces of holomorphic disks with boundary on an exact Lagrangian immersion of a spin manifold into complex n-space in a coherent manner. This allows us to lift the coefficients of the contact homology of Legendrian spin submanifolds of standard contact (2n + 1)-space from ℤ2 to ℤ. We demonstrate how the ℤ-lift provides a more refined invariant of Legendrian isotopy. We also apply contact homology to produce lower bounds on double points of certain exact Lagrangian immersions into ℂn and again including orientations strengthens the results. More precisely, we prove that the number of double points of an exact Lagrangian immersion of a closed manifold M whose associated Legendrian embedding has good DGA is at least half of the dimension of the homology of M with coefficients in an arbitrary field if M is spin and in ℤ2 otherwise.
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CHEN, B. Y., F. DILLEN, L. VERSTRAELEN, and L. VRANCKEN. "Lagrangian isometric immersions of a real-space-form Mn(c) into a complex-space-form M˜n(4c)." Mathematical Proceedings of the Cambridge Philosophical Society 124, no. 1 (July 1998): 107–25. http://dx.doi.org/10.1017/s030500419700217x.

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It is well known that totally geodesic Lagrangian submanifolds of a complex-space-form M˜n(4c) of constant holomorphic sectional curvature 4c are real-space-forms of constant sectional curvature c. In this paper we investigate and determine non-totally geodesic Lagrangian isometric immersions of real-space-forms of constant sectional curvature c into a complex-space-form M˜n(4c). In order to do so, associated with each twisted product decomposition of a real-space-form of the form f1I1×… ×fkIk×1Nn−k(c), we introduce a canonical 1-form, called the twistor form of the twisted product decomposition. Roughly speaking, our main result says that if the twistor form of such a twisted product decomposition of a simply-connected real-space-form of constant sectional curvature c is twisted closed, then it admits a ‘unique’ adapted Lagrangian isometric immersion into a complex-space-form M˜n(4c). Conversely, if L: Mn(c)→ M˜n(4c) is a non-totally geodesic Lagrangian isometric immersion of a real-space-form Mn(c) of constant sectional curvature c into a complex-space-form M˜n(4c), then Mn(c) admits an appropriate twisted product decomposition with twisted closed twistor form and, moreover, the Lagrangian immersion L is given by the corresponding adapted Lagrangian isometric immersion of the twisted product. In this paper we also provide explicit constructions of adapted Lagrangian isometric immersions of some natural twisted product decompositions of real-space-forms.
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Marbes, Heinz. "On the Set of Umbilical Points of a Twistor-Holomorphic Immersion IntoR4." Mathematische Nachrichten 142, no. 1 (1989): 19–26. http://dx.doi.org/10.1002/mana.19891420103.

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Hasegawa, Kazuyuki. "The first Chern class and conformal area for a twistor holomorphic immersion." Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 84, no. 1 (January 22, 2014): 67–83. http://dx.doi.org/10.1007/s12188-014-0089-3.

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Ando, Naoya. "Local characterizations of complex curves in C2 and sphere Schwarz maps." International Journal of Mathematics 27, no. 08 (July 2016): 1650067. http://dx.doi.org/10.1142/s0129167x16500671.

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In this paper, we obtain a local characterization of a complex curve in [Formula: see text] in terms of the induced metric and a holomorphic cubic differential [Formula: see text], and we see that any complex curve in [Formula: see text] is locally represented as the image by the composition of an affine Schwarz map and a parallel translation in [Formula: see text]. We obtain a local characterization of a sphere Schwarz immersion in terms of a positive-valued function [Formula: see text].
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Dissertations / Theses on the topic "Holomorphic immersion"

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Loi, Andrea. "Quantization of Kaehler manifolds and holomorphic immersions in projective spaces." Thesis, University of Warwick, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263632.

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Sridharan, Haripriya. "Spaces of Holomorphic Immersions of Open Riemann Surfaces into the Complex Plane." Thesis, 2020. http://hdl.handle.net/2440/125739.

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Let M be an open Riemann surface. A recent result due to Forstneriˇc and L´arusson [8] says that, for a closed conical subvariety A ⇢ Cn such that A \ {0} is an Oka manifold, the weak homotopy type of the space of non-degenerate holomorphic A-immersions of M into Cn is the same as that of the space of holomorphic (or equivalently, continuous) maps from M into A\{0}. In their paper, the authors sketch the proof of this theoremthrough claiming analogy with a related result, and invoking advanced results from complex and di↵erential geometry, including seminal theorems from Oka theory. The work contained in this thesis was motivated by the absence of a self-contained proof for the special case where A = C – as, perhaps, the first geometrically interesting case that one would consider. We remedy the absence by providing a fully detailed, self-contained proof of this case; namely, the parametric h-principle for holomorphic immersions of open Riemann surfaces into C. We outline this more precisely as follows. Take a holomorphic 1-form ✓ on M which vanishes nowhere. We denote by I(M,C) the space of holomorphic immersions of M into C, and denote by O(M,C⇤) the space of nonvanishing holomorphic functions on M. We prove, in all detail, that the continuous map I(M,C)!O(M,C⇤), f 7! df /✓, is a weak homotopy equivalence. This gives a full description of the weak homotopy type of I(M,C), as the target space O(M,C⇤) is known by algebraic topology (Remark 5.2.3).
Thesis (MPhil) -- University of Adelaide, School of Mathematical Sciences, 2020
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John, Daniel. "Holomorphic Immersions of Restricted Growth from Smooth Affine Algebraic Curves into the Complex Plane." Thesis, 2019. http://hdl.handle.net/2440/119912.

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We investigate immersions of restricted growth from affine curves into the complex plane. We focus on the finite order and algebraic categories. In the finite order case we prove a generalisation of a result due to Forstneric and Ohsawa, showing that on every affine curve there is a finite order 1-form with prescribed periods and divisor, provided we restrict the growth of the divisor at the punctures. We also enumerate the algebraic immersions of triply punctured compact surfaces into the complex plane using the theory of dessins d’enfants and obtain an upper bound on the number of surfaces that admit such an immersion.
Thesis (MPhil.) -- University of Adelaide, School of Mathematical Sciences, 2019
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Perrier, Alexandre. "Groupes de cobordisme lagrangien immergé et structure des polygones pseudo-holomorphes." Thèse, 2018. http://hdl.handle.net/1866/21747.

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Books on the topic "Holomorphic immersion"

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Bismut, Jean-Michel. Holomorphic families of immersions and higher analytic torsion forms. Paris: Société mathématique de France, 1997.

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Bismut, Jean-Michel. Holomorphic families of immersions and higher analytic torsion forms. Paris: Société mathématique de France, 1997.

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Loi, Andrea. Quantization of Kähler manifolds and holomorphic immersions in projective spaces. [s.l.]: typescript, 1997.

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Book chapters on the topic "Holomorphic immersion"

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Forstnerič, Franc. "Embeddings, Immersions and Submersions." In Stein Manifolds and Holomorphic Mappings, 403–76. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61058-0_9.

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Forstnerič, Franc. "Embeddings, Immersions and Submersions." In Stein Manifolds and Holomorphic Mappings, 333–400. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22250-4_8.

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Forstnerič, Franc. "Holomorphic Embeddings and Immersions of Stein Manifolds: A Survey." In Springer Proceedings in Mathematics & Statistics, 145–69. Singapore: Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-1672-2_11.

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Mok, Ngaiming. "On singularities of generically immersive holomorphic maps between complex hyperbolic space forms." In Complex and Differential Geometry, 323–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-20300-8_16.

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MATSUSHIMA, YOZO. "HOLOMORPHIC IMMERSIONS OF A COMPACT KÄHLER MANIFOLD INTO COMPLEX TORI." In Collected Papers of Y Matsushima, 614–33. WORLD SCIENTIFIC, 1992. http://dx.doi.org/10.1142/9789814360067_0043.

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