Relevant bibliographies by topics / Compact smooth manifold

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Compact smooth manifold'

Author: Grafiati
Published: 30 May 2022
Last updated: 31 May 2022

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Journal articles on the topic "Compact smooth manifold"

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CALCUT, J. S. "TORELLI ACTIONS AND SMOOTH STRUCTURES ON FOUR MANIFOLDS." Journal of Knot Theory and Its Ramifications 17, no. 02 (February 2008): 171–90. http://dx.doi.org/10.1142/s0218216508006075.

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Artin presentations are discrete equivalents of planar open book decompositions of closed, orientable three manifolds. Artin presentations characterize the fundamental groups of closed, orientable three manifolds. An Artin presentation also determines a smooth, compact, simply conected four manifold that bounds the three dimensional open book. In this way, the study of three and four manifolds may be approached purely group theoretically. In the theory of Artin presentations, elements of the Torelli subgroup act on the topology and smooth structures of the three and four manifolds. We show that the Torelli action can preserve the continuous topological type of a four manifold while changing its smooth structure. This is a new, group theoretic method of altering the smooth structure on a four manifold.
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Silver, Daniel S. "Examples of 3-knots with no minimal Seifert manifolds." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 3 (November 1991): 417–20. http://dx.doi.org/10.1017/s0305004100070481.

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We work throughout in the smooth category. Homomorphisms of fundamental and homology groups are induced by inclusion. Ann-knot, formn≥ 1, is an embeddedn-sphereK⊂Sn+2. ASeifert manifoldforKis a compact, connected, orientable (n+ 1)-manifoldV⊂Sn+2with boundary ∂V=K. By [9] Seifert manifolds always exist. As in [9] letYdenoteSn+2split alongV; Yis a compact manifold with ∂Y=V0∪V1, whereVt≈V. We say thatVis aminimal Seifert manifoldforKif π1Vt→ π1Yis a monomorphism fort= 0, 1. (Here and throughout basepoint considerations are suppressed.)
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JOST, JÜRGEN, and YI-HU YANG. "KÄHLER MANIFOLDS AND FUNDAMENTAL GROUPS OF NEGATIVELY δ-PINCHED MANIFOLDS." International Journal of Mathematics 15, no. 02 (March 2004): 151–67. http://dx.doi.org/10.1142/s0129167x04002247.

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In this note, we will show that the fundamental group of any negatively δ-pinched [Formula: see text] manifold cannot be the fundamental group of a quasi-compact Kähler manifold. As a consequence of our proof, we also show that any nonuniform lattice in F4(-20) cannot be the fundamental group of a quasi-compact Kähler manifold. The corresponding result for uniform lattices was proved by Carlson and Hernández [3]. Finally, we follow Gromov and Thurston [6] to give some examples of negatively δ-pinched manifolds [Formula: see text] of finite volume which, as topological manifolds, admit no hyperbolic metric with finite volume under any smooth structure. This shows that our result for δ-pinched manifolds is a nontrivial generalization of the fact that no nonuniform lattice in SO(n,1)(n≥3) is the fundamental group of a quasi-compact Kähler manifold [21].
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Alpern, S., and V. Prasad. "End Behaviour and Ergodicity for Homeomorphisms of Manifolds with Finitely Many Ends." Canadian Journal of Mathematics 39, no. 2 (April 1, 1987): 473–91. http://dx.doi.org/10.4153/cjm-1987-020-5.

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The recent paper of Berlanga and Epstein [5] demonstrated the significant role played by the “ends” of a noncompact manifold M in answering questions relating homeomorphisms of M to measures on M. In this paper we show that an analysis of the end behaviour of measure preserving homeomorphisms of a manifold also leads to an understanding of some of their ergodic properties, and allows results previously obtained for compact manifolds to be extended (with qualifications) to the noncompact case. We will show that ergodicity is typical (dense Gδ) with respect to various compact-open topology closed subsets of the space consisting of all homeomorphisms of a manifold M which preserve a measure μ. It may be interesting for topologists to note that we prove when M is a σ-compact connected n-manifold, n≧ 2, then M is the countable union of an increasing family of compact connected manifolds. If M is a PL or smooth manifold, this is well known and easy. If M is just, however, a topological n-manifold then we apply the recent results [9] and [12] to prove the result. The Borel measure μ, is taken to be nonatomic, locally finite, positive on open sets, and zero for the manifold boundary of M.
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Katok, Anatole, and Keith Burns. "Infinitesimal Lyapunov functions, invariant cone families and stochastic properties of smooth dyanmical systems." Ergodic Theory and Dynamical Systems 14, no. 4 (December 1994): 757–85. http://dx.doi.org/10.1017/s0143385700008142.

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AbstractWe establish general criteria for ergodicity and Bernoulliness for volume preserving diffeormorphisms and flows on compact manifolds. We prove that every ergodic component with non-zero Lyapunov exponents of a contact flow is Bernoulli. As an application of our general results, we construct on every compact 3-dimensional manifold a C∞ Riemannian metric whose geodesic flow is Bernoulli.
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Dancer, Andrew, and Andrew Swann. "The Geometry of Singular Quaternionic Kähler Quotients." International Journal of Mathematics 08, no. 05 (August 1997): 595–610. http://dx.doi.org/10.1142/s0129167x97000317.

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Two descriptions of quaternionic Kähler quotients by proper group actions are given: the first as a union of smooth manifolds, some of which come equipped with quaternionic Kähler or locally Kähler structures; the second as a union of quaternionic Kähler orbifolds. In particular the quotient always has an open set which is a smooth quaternionic Kähler manifold. When the original manifold and the group are compact, we describe a length space structure on the quotient. Similar descriptions of singular hyperKähler and 3-Sasakian quotients are given.
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Lee, Manseob. "Positively Continuum-Wise Expansiveness for C1 Differentiable Maps." Mathematics 7, no. 10 (October 16, 2019): 980. http://dx.doi.org/10.3390/math7100980.

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We show that if a differentiable map f of a compact smooth Riemannian manifold M is C 1 robustly positive continuum-wise expansive, then f is expanding. Moreover, C 1 -generically, if a differentiable map f of a compact smooth Riemannian manifold M is positively continuum-wise expansive, then f is expanding.
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Glöckner, Helge, and Alexander Schmeding. "Manifolds of mappings on Cartesian products." Annals of Global Analysis and Geometry 61, no. 2 (January 5, 2022): 359–98. http://dx.doi.org/10.1007/s10455-021-09816-y.

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AbstractGiven smooth manifolds $$M_1,\ldots , M_n$$ M 1 , … , M n (which may have a boundary or corners), a smooth manifold N modeled on locally convex spaces and $$\alpha \in ({{\mathbb {N}}}_0\cup \{\infty \})^n$$ α ∈ ( N 0 ∪ { ∞ } ) n , we consider the set $$C^\alpha (M_1\times \cdots \times M_n,N)$$ C α ( M 1 × ⋯ × M n , N ) of all mappings $$f:M_1\times \cdots \times M_n\rightarrow N$$ f : M 1 × ⋯ × M n → N which are $$C^\alpha $$ C α in the sense of Alzaareer. Such mappings admit, simultaneously, continuous iterated directional derivatives of orders $$\le \alpha _j$$ ≤ α j in the jth variable for $$j\in \{1,\ldots , n\}$$ j ∈ { 1 , … , n } , in local charts. We show that $$C^\alpha (M_1\times \cdots \times M_n,N)$$ C α ( M 1 × ⋯ × M n , N ) admits a canonical smooth manifold structure whenever each $$M_j$$ M j is compact and N admits a local addition. The case of non-compact domains is also considered.
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Guan, Daniel. "Type II compact almost homogeneous manifolds of cohomogeneity one-II." International Journal of Mathematics 30, no. 13 (December 2019): 1940002. http://dx.doi.org/10.1142/s0129167x19400020.

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In this paper, we start the program of the existence of the smooth equivariant geodesics in the equivariant Mabuchi moduli space of Kähler metrics on type II cohomogeneity one compact Kähler manifold. In this paper, we deal with the manifolds [Formula: see text] obtained by blowing up the diagonal of the product of two copies of a [Formula: see text].
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Kołodziej, Sławomir, and Ngoc Cuong Nguyen. "Weak solutions of complex Hessian equations on compact Hermitian manifolds." Compositio Mathematica 152, no. 11 (September 9, 2016): 2221–48. http://dx.doi.org/10.1112/s0010437x16007417.

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We prove the existence of weak solutions of complex $m$-Hessian equations on compact Hermitian manifolds for the non-negative right-hand side belonging to $L^{p}$, $p>n/m$ ($n$ is the dimension of the manifold). For smooth, positive data the equation has recently been solved by Székelyhidi and Zhang. We also give a stability result for such solutions.
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Dissertations / Theses on the topic "Compact smooth manifold"

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Іванов, Сергій Миколайович. "Аналіз локальних властивостей динаміки автономних систем на компактному гладкому многовиді." Doctoral thesis, Київ, 2019. https://ela.kpi.ua/handle/123456789/32131.

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Робота виконана в Інституті космічних досліджень Національної академії наук України (ІКД НАНУ) та Державного космічного агентства України.
Дисертаційна робота присвячена дослідженню актуальних проблем в області аналізу автономних систем. Досліджується локальна структурна стійкість (орбітально топологічна еквівалентність), локальна (в околі точки положення рівноваги) дифеоморфність динамічних систем на компактному гладкому многовиді, які описуються звичайними диференціальними рівняннями (автономними системами), а також фрактальна розмірність Каплана-Йоркі. Математично обґрунтовано метод оцінювання локальної матриці Якобі та обчислення експонент Ляпунова. Проводиться аналіз і обчислення експонент Ляпунова, розмірності та граничної ентропії для геомагнітних індексів Dst, Kp, AE, які мають ознаки гіперхаотичної динаміки.
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Book chapters on the topic "Compact smooth manifold"

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Gorodski, Claudio. "Smooth Manifolds." In Compact Textbooks in Mathematics, 1–45. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-49775-0_1.

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Alessandrini, Lucia, and Giovanni Bassanelli. "Smooth proper modifications of compact Kähler manifolds." In Complex Analysis, 1–7. Wiesbaden: Vieweg+Teubner Verlag, 1991. http://dx.doi.org/10.1007/978-3-322-86856-5_1.

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Güneysu, Batu. "Smooth Compactly Supported Sections as Form Core." In Covariant Schrödinger Semigroups on Riemannian Manifolds, 163–65. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68903-6_13.

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Liu, Xu. "Compact Smooth but Non-complex Complements of Complete Kähler Manifolds." In Complex Analysis and Geometry, 235–39. Tokyo: Springer Japan, 2015. http://dx.doi.org/10.1007/978-4-431-55744-9_17.

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Pawalowski, Krzysztof. "Manifolds as Fixed Point Sets of Smooth Compact Lie Group Actions." In K-Monographs in Mathematics, 79–104. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-009-0003-5_6.

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"The Hodge theory of a smooth, oriented, compact Riemannian manifold." In The Hodge Theory of Projective Manifolds, 19–25. PUBLISHED BY IMPERIAL COLLEGE PRESS AND DISTRIBUTED BY WORLD SCIENTIFIC PUBLISHING CO., 2007. http://dx.doi.org/10.1142/9781860948657_0002.

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Bär, Christian, and Sebastian Hannes. "Boundary Value Problems for the Lorentzian Dirac Operator." In Geometry and Physics: Volume I, 3–18. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198802013.003.0001.

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On a compact globally hyperbolic Lorentzian spin manifold with smooth space-like Cauchy boundary, the (hyperbolic) Dirac operator is known to be Fredholm when Atiyah–Patodi–Singer boundary conditions are imposed. This chapter explores to what extent these boundary conditions can be replaced by more general ones and how the index then changes. There are some differences to the classical case of the elliptic Dirac operator on a Riemannian manifold with boundary.
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Tu, Loring W. "The Topology of a Group Action." In Introductory Lectures on Equivariant Cohomology, 205–12. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.003.0025.

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This chapter describes the topology of a group action. It proves some topological facts about the fixed point set and the stabilizers of a continuous or a smooth action. The chapter also introduces the equivariant tubular neighborhood theorem and the equivariant Mayer–Vietoris sequence. A tubular neighborhood of a submanifold S in a manifold M is a neighborhood that has the structure of a vector bundle over S. Because the total space of a vector bundle has the same homotopy type as the base space, in calculating cohomology one may replace a submanifold by a tubular neighborhood. The tubular neighborhood theorem guarantees the existence of a tubular neighborhood for a compact regular submanifold. The Mayer–Vietoris sequence is a powerful tool for calculating the cohomology of a union of two open subsets. Both the tubular neighborhood theorem and the Mayer–Vietoris sequence have equivariant counterparts for a G-manifold where G is a compact Lie group.
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"Compact embedded smooth manifolds." In Graduate Studies in Mathematics, 107–31. Providence, Rhode Island: American Mathematical Society, 2021. http://dx.doi.org/10.1090/gsm/218/06.

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Tu, Loring W. "Integration on a Compact Connected Lie Group." In Introductory Lectures on Equivariant Cohomology, 103–14. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.003.0013.

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This chapter explores integration on a compact connected Lie group. One of the great advantages of working with a compact Lie group is the possibility of extending the notion of averaging from a finite group to the compact Lie group. If the compact Lie group is connected, then there exists a unique bi-invariant top-degree form with total integral 1, which simplifies the presentation of averaging. The averaging operator is useful for constructing invariant objects. For example, suppose a compact connected Lie group G acts smoothly on the left on a manifold M. Given any C∞ differential k-form ω‎ on M, by averaging all the left translates of ω‎ over G, one can produce a C∞ invariant k-form on M. As another example, on a G-manifold one can average all translates of a Riemannian metric to produce an invariant Riemann metric.
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Conference papers on the topic "Compact smooth manifold"

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Szilak, Karoly. "A non-smooth Neumann problem on compact Riemannian manifolds." In 2021 IEEE 15th International Symposium on Applied Computational Intelligence and Informatics (SACI). IEEE, 2021. http://dx.doi.org/10.1109/saci51354.2021.9465567.

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Ehler, Martin, and Manuel Graf. "Numerically Optimizing Weights for Monte Carlo Integration on Smooth Compact Manifolds." In 2017 19th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC). IEEE, 2017. http://dx.doi.org/10.1109/synasc.2017.00071.

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Jokar, Amir, Steven J. Eckels, and Mohammad H. Hosni. "Evaluation of Heat Transfer and Pressure Drop for the Heater-Core in an Automotive Heat Pump System." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-60824.

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The heat transfer and pressure drop results for a heater-core of an automotive system are presented and discussed in this article. The heater-core is a type of compact heat exchanger that is used as part of an automobile heating-cooling system for heating the passenger cabin on cold seasons. The automotive heating-cooling system in this study includes a standard refrigeration cycle consists of a condenser, an evaporator, a compressor and an expansion valve using the refrigerant R134a as the working fluid. Furthermore, the system uses two separate secondary fluid loops using a 50% glycol-water mixture to exchange energy with the main refrigeration loop. During the cold weather season, the system is operated in the heat pump mode and one of the fluid loops is used to transfer heat from the condenser to the heater-core for heating the passenger cabin. The heat transfer from the heater-core to the passenger cabin is accomplished using air flow through the heater-core openings in an unmixed and cross-flow fashion. The air-side of the heater-core has a unique louver system that is intended to enhance the air-side heat transfer while the glycol-side has a twisted wire inserts to enhance flow turbulence and heat transfer. Semi-empirical correlations for the heat transfer and pressure drop for both glycol-water mixture and air flows in the heater-core are proposed. The flow of the glycol-water mixture in the heater-core is a single-phase flow within a bundle of parallel circular tubes with the twisted wire inserts. The flow of air through the heater-core is approximated as a flow across a finned-tube compact heat exchanger with continuous plate-fins. A modified Wilson plot technique is applied to determine correlations for heat transfer on both glycol-water mixture and air sides. The frictional pressure drop on the glycol-side is calculated from the total measured pressure drop and adjusted for pressure drops within manifolds and inlet/outlet ports. The results for the heat transfer and pressure drop analyses are finally plotted, discussed and compared with the relevant previous studies. These results show that the heat transfer rate is increased in the glycol-side due to the twisted wire inserts, in comparison with the smooth circular tubes. The air-side heat transfer rate is also enhanced due to the louvers in the air passages, as compared to flat-plate fins in compact heat exchangers.
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