Two Classes Of Riemannian Manifolds Whose Geodesic Flows Are Integrable
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Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable by Kazuyoshi Kiyohara Pdf
In this work, two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and Kahler-Liouville manifolds respectively. In each case, the author finds several invariants with which they are partly classified. The classification indicates, in particular, that these classes contain many new examples of manifolds with integrable geodesic flow.
Periodic Hamiltonian Flows on Four Dimensional Manifolds by Yael Karshon Pdf
Abstract - we classify the periodic Hamiltonian flows on compact four dimensional symplectic manifolds up to isomorphism of Hamiltonian $S^1$-spaces. Additionally, we show that all these spaces are Kahler, that every such space is obtained from a simple model by a sequence of symplectic blowups, and that if the fixed points are isolated then the space is a toric variety.
David M Calderbank,Michael G. Eastwood,Vladimir S. Matveev,Katharina Neusser
Author : David M Calderbank,Michael G. Eastwood,Vladimir S. Matveev,Katharina Neusser Publisher : American Mathematical Society Page : 137 pages File Size : 43,6 Mb Release : 2021-02-10 Category : Mathematics ISBN : 9781470443009
C-Projective Geometry by David M Calderbank,Michael G. Eastwood,Vladimir S. Matveev,Katharina Neusser Pdf
The authors develop in detail the theory of (almost) c-projective geometry, a natural analogue of projective differential geometry adapted to (almost) complex manifolds. The authors realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kähler manifold gives rise to a c-projective structure and this is one of the primary motivations for its study. The existence of two or more Kähler metrics underlying a given c-projective structure has many ramifications, which the authors explore in depth. As a consequence of this analysis, they prove the Yano–Obata Conjecture for complete Kähler manifolds: if such a manifold admits a one parameter group of c-projective transformations that are not affine, then it is complex projective space, equipped with a multiple of the Fubini-Study metric.
Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space by Peter W. Bates,Kening Lu,Chongchun Zeng Pdf
Extends the theory for normally hyperbolic invariant manifolds to infinite dimensional dynamical systems in a Banach space, thereby providing tools for the study of PDE's and other infinite dimensional equations of evolution. In the process, the authors establish the existence of center-unstable and center-stable manifolds in a neighborhood of the unperturbed compact manifold. No index. Annotation copyrighted by Book News, Inc., Portland, OR
The Integral Manifolds of the Three Body Problem by Christopher Keil McCord,Kenneth Ray Meyer,Quidong Wang Pdf
The phase space of the spatial three-body problem is an open subset in ${\mathbb R}^{18}$. Holding the ten classical integrals of energy, center of mass, linear and angular momentum fixed defines an eight dimensional submanifold. For fixed nonzero angular momentum, the topology of this manifold depends only on the energy. This volume computes the homology of this manifold for all energy values. This table of homology shows that for negative energy, the integral manifolds undergo seven bifurcations. Four of these are the well-known bifurcations due to central configurations, and three are due to 'critical points at infinity'. This disproves Birkhoff's conjecture that the bifurcations occur only at central configurations.
The Siegel Modular Variety of Degree Two and Level Four by Ronnie Lee,Steven H. Weintraub,Jerome William Hoffman Pdf
The Siegel Modular Variety of Degree Two and Level Four is by Ronnie Lee and Steven H. Weintraub: Let $\mathbf M_n$ denote the quotient of the degree two Siegel space by the principal congruence subgroup of level $n$ of $Sp_4(\mathbb Z)$. $\mathbfM_n$ is the moduli space of principally polarized abelian surfaces with a level $n$ structure and has a compactification $\mathbfM^*_n$ first constructed by Igusa. $\mathbfM^*_n$ is an almost non-singular (non-singular for $n> 1$) complex three-dimensional projective variety (of general type, for $n> 3$). The authors analyze the Hodge structure of $\mathbfM^*_4$, completely determining the Hodge numbers $h^{p,q} = \dim H^{p,q}(\mathbfM^*_4)$. Doing so relies on the understanding of $\mathbfM^*_2$ and exploitation of the regular branched covering $\mathbfM^*_4 \rightarrow \mathbfM^*_2$.""Cohomology of the Siegel Modular Group of Degree Two and Level Four"" is by J. William Hoffman and Steven H. Weintraub. The authors compute the cohomology of the principal congruence subgroup $\Gamma_2(4) \subset S{_p4} (\mathbb Z)$ consisting of matrices $\gamma \equiv \mathbf 1$ mod 4. This is done by computing the cohomology of the moduli space $\mathbfM_4$. The mixed Hodge structure on this cohomology is determined, as well as the intersection cohomology of the Satake compactification of $\mathbfM_4$.
Almost Automorphic and Almost Periodic Dynamics in Skew-Product Semiflows by Wenxian Shen,Yingfei Yi Pdf
This volume is devoted to the study of almost automorphic dynamics in differential equations. By making use of techniques from abstract topological dynamics, it is shown that almost automorphy, a notion which was introduced by S. Bochner in 1955, is essential and fundamental in the qualitative study of almost periodic differential equations.
Conjugacy of Alt5 and SL(2, 5) Subgroups of E8(C) by Darrin D. Frey Pdf
Exceptional complex Lie groups have become increasingly important in various fields of mathematics and physics. As a result, there has been interest in expanding the representation theory of finite groups to include embeddings into the exceptional Lie groups. Cohen, Griess, Lisser, Ryba, Serre and Wales have pioneered this area, classifying the finite simple and quasisimple subgroups that embed in the exceptional complex Lie groups. This work contains the first major results concerning conjugacy classes of embeddings of finite subgroups of an exceptional complex Lie group in which there are large numbers of classes. The approach developed in this work is character theoretic, taking advantage of the classical subgroups of $E_8 (\mathbb C)$. The machinery used is relatively elementary and has been used by the author and others to solve other conjugacy problems. The results presented here are very explicit. Each known conjugacy class is listed by its fusion pattern with an explicit character afforded by an embedding in that class.
Algebraic Structure of Pseudocompact Groups by Dikran N. Dikranjan,Dmitri Shakhmatov Pdf
The fundamental property of compact spaces - that continuous functions defined on compact spaces are bounded - served as a motivation for E. Hewitt to introduce the notion of a pseudocompact space. The class of pseudocompact spaces proved to be of fundamental importance in set-theoretic topology and its applications. This clear and self-contained exposition offers a comprehensive treatment of the question, When does a group admit an introduction of a pseudocompact Hausdorff topology that makes group operations continuous? Equivalently, what is the algebraic structure of a pseudocompact Hausdorff group? The authors have adopted a unifying approach that covers all known results and leads to new ones, Results in the book are free of any additional set-theoretic assumptions.
Spectral Asymptotics on Degenerating Hyperbolic 3-Manifolds by Józef Dodziuk,Jay Jorgenson Pdf
In this volume, the authors study asymptotics of the geometry and spectral theory of degenerating sequences of finite volume hyperbolic manifolds of three dimensions. Thurston's hyperbolic surgery theorem assets the existence of non-trivial sequences of finite volume hyperbolic three manifolds which converge to a three manifold with additional cusps. In the geometric aspect of their study, the authors use the convergence of hyperbolic metrics on the thick parts of the manifolds under consideration to investigate convergentce of tubes in the manifolds of the sequence to cusps of the limiting manifold. In the specral theory aspect of the work, they prove convergence of heat kernels. They then define a regualrized heat race associated to any finite volume, complete, hyperbolic three manifold, and study its asymptotic behaviour through degeneration. As an application of the analysis of the regularized heat trace, they study asymptotic behaviours of the spectral zeta function, determinant of the Laplacian, Selberg zeta function, and spectral counting functions through degeneration. The authors' methods are an adaptation to three dimensions of the earlier work of Jorgenson and Lundelius who investigated the asymptotic behaviour of spectral functions on degenerating families of finite area hyperbolic Riemann surfaces.
Prospects Of Differential Geometry And Its Related Fields - Proceedings Of The 3rd International Colloquium On Differential Geometry And Its Related Fields by Toshiaki Adachi,Hideya Hashimoto,Milen J Hristov Pdf
This volume consists of contributions by the main participants of the 3rd International Colloquium on Differential Geometry and its Related Fields (ICDG2012), which was held in Veliko Tarnovo, Bulgaria. Readers will find original papers by specialists and well-organized reports of recent developments in the fields of differential geometry, complex analysis, information geometry, mathematical physics and coding theory. This volume provides significant information that will be useful to researchers and serves as a good guide for young scientists. It is also for those who wish to start investigating these topics and interested in their interdisciplinary areas.
On Stability and Endoscopic Transfer of Unipotent Orbital Integrals on $p$-adic Symplectic Groups by Magdy Assem Pdf
The invariant integrals of spherical functions over certain infinite families of unipotent orbits in symplectic groups over a p-adic field of characteristic zero are explicitly calculated. The results are then put into a conjectural framework that predicts for split classical groups which linear combinations of unipotent orbital integrals are stable distributions. No index. Annotation copyrighted by Book News, Inc., Portland, OR
