Two Classes Of Riemannian Manifolds Whose Geodesic Flows Are Integrable
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Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable
Author | : Kazuyoshi Kiyohara |
Publsiher | : American Mathematical Soc. |
Total Pages | : 143 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 9780821806401 |
Download Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable Book in PDF, Epub and Kindle
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
Author | : Yael Karshon |
Publsiher | : American Mathematical Soc. |
Total Pages | : 71 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 9780821811818 |
Download Periodic Hamiltonian Flows on Four Dimensional Manifolds Book in PDF, Epub and Kindle
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.
C Projective Geometry
Author | : David M Calderbank,Michael G. Eastwood,Vladimir S. Matveev,Katharina Neusser |
Publsiher | : American Mathematical Society |
Total Pages | : 137 |
Release | : 2021-02-10 |
Genre | : Mathematics |
ISBN | : 9781470443009 |
Download C Projective Geometry Book in PDF, Epub and Kindle
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
Author | : Peter W. Bates,Kening Lu,Chongchun Zeng |
Publsiher | : American Mathematical Soc. |
Total Pages | : 145 |
Release | : 1998 |
Genre | : Differentiable dynamical systems |
ISBN | : 9780821808689 |
Download Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space Book in PDF, Epub and Kindle
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
Author | : Christopher Keil McCord,Kenneth Ray Meyer,Quidong Wang |
Publsiher | : American Mathematical Soc. |
Total Pages | : 91 |
Release | : 1998 |
Genre | : Science |
ISBN | : 9780821806920 |
Download The Integral Manifolds of the Three Body Problem Book in PDF, Epub and Kindle
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
Author | : Ronnie Lee,Steven H. Weintraub,Jerome William Hoffman |
Publsiher | : American Mathematical Soc. |
Total Pages | : 75 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 9780821806203 |
Download The Siegel Modular Variety of Degree Two and Level Four Book in PDF, Epub and Kindle
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
Author | : Wenxian Shen,Yingfei Yi |
Publsiher | : American Mathematical Soc. |
Total Pages | : 111 |
Release | : 1998 |
Genre | : Flows (Differentiable dynamical systems). |
ISBN | : 9780821808672 |
Download Almost Automorphic and Almost Periodic Dynamics in Skew Product Semiflows Book in PDF, Epub and Kindle
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.
The Defect Relation of Meromorphic Maps on Parabolic Manifolds
Author | : George Lawrence Ashline |
Publsiher | : American Mathematical Soc. |
Total Pages | : 78 |
Release | : 1999 |
Genre | : Mathematics |
ISBN | : 9780821810699 |
Download The Defect Relation of Meromorphic Maps on Parabolic Manifolds Book in PDF, Epub and Kindle
This book is intended for graduate students and research mathematicians working in several complex variables and analytic spaces.