Global Affine Differential Geometry Of Hypersurfaces
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Global Affine Differential Geometry Of Hypersurfaces
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Author : An-Min Li
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-08-17
Global Affine Differential Geometry Of Hypersurfaces written by An-Min Li and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-17 with Mathematics categories.
This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. Moreover, the recent development revealed that affine differential geometry – as differential geometry in general – has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces. The second edition of this monograph leads the reader from introductory concepts to recent research. Since the publication of the first edition in 1993 there appeared important new contributions, like the solutions of two different affine Bernstein conjectures, due to Chern and Calabi, respectively. Moreover, a large subclass of hyperbolic affine spheres were classified in recent years, namely the locally strongly convex Blaschke hypersurfaces that have parallel cubic form with respect to the Levi-Civita connection of the Blaschke metric. The authors of this book present such results and new methods of proof.
Affine Bernstein Problems And Monge Amp Re Equations
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Author : An-Min Li
language : en
Publisher: World Scientific
Release Date : 2010
Affine Bernstein Problems And Monge Amp Re Equations written by An-Min Li and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
In this monograph, the interplay between geometry and partial differential equations (PDEs) is of particular interest. It gives a selfcontained introduction to research in the last decade concerning global problems in the theory of submanifolds, leading to some types of Monge-AmpFre equations. From the methodical point of view, it introduces the solution of certain Monge-AmpFre equations via geometric modeling techniques. Here geometric modeling means the appropriate choice of a normalization and its induced geometry on a hypersurface defined by a local strongly convex global graph. For a better understanding of the modeling techniques, the authors give a selfcontained summary of relative hypersurface theory, they derive important PDEs (e.g. affine spheres, affine maximal surfaces, and the affine constant mean curvature equation). Concerning modeling techniques, emphasis is on carefully structured proofs and exemplary comparisons between different modelings.
Affine Differential Geometry
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Author : Katsumi Nomizu
language : en
Publisher: Cambridge University Press
Release Date : 1994-11-10
Affine Differential Geometry written by Katsumi Nomizu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-11-10 with Mathematics categories.
This is a self-contained and systematic account of affine differential geometry from a contemporary viewpoint, not only covering the classical theory, but also introducing the modern developments that have happened over the last decade. In order both to cover as much as possible and to keep the text of a reasonable size, the authors have concentrated on the significant features of the subject and their relationship and application to such areas as Riemannian, Euclidean, Lorentzian and projective differential geometry. In so doing, they also provide a modern introduction to the last. Some of the important geometric surfaces considered are illustrated by computer graphics, making this a physically and mathematically attractive book for all researchers in differential geometry, and for mathematical physicists seeking a quick entry into the subject.
Geometry And Topology Of Submanifolds Ix
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Author : Leopold Verstraelen
language : en
Publisher: World Scientific
Release Date : 1999-07-22
Geometry And Topology Of Submanifolds Ix written by Leopold Verstraelen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-22 with Mathematics categories.
Contents:Affine Bibliography 1998 (T Binder et al.)Contact Metric R-Harmonic Manifolds (K Arslan & C Murathan)Local Classification of Centroaffine Tchebychev Surfaces with Constant Curvature Metric (T Binder)Hypersurfaces in Space Forms with Some Constant Curvature Functions (F Brito et al.)Some Relations Between a Submanifold and Its Focal Set (S Carter & A West)On Manifolds of Pseudosymmetric Type (F Defever et al.)Hypersurfaces with Pseudosymmetric Weyl Tensor in Conformally Flat Manifolds (R Deszcz et al.)Least-Squares Geometrical Fitting and Minimising Functions on Submanifolds (F Dillen et al.)Cubic Forms Generated by Functions on Projectively Flat Spaces (J Leder)Distinguished Submanifolds of a Sasakian Manifold (I Mihai)On the Curvature of Left Invariant Locally Conformally Para-Kählerian Metrics (Z Olszak)Remarks on Affine Variations on the Ellipsoid (M Wiehe)Dirac's Equation, Schrödinger's Equation and the Geometry of Surfaces (T J Willmore)and other papers Readership: Researchers doing differential geometry and topology. Keywords:Proceedings;Geometry;Topology;Valenciennes (France);Lyon (France);Leuven (Belgium);Dedication
Global Differential Geometry And Global Analysis
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Author : Dirk Ferus
language : en
Publisher: Springer
Release Date : 2006-11-14
Global Differential Geometry And Global Analysis written by Dirk Ferus and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
All papers appearing in this volume are original research articles and have not been published elsewhere. They meet the requirements that are necessary for publication in a good quality primary journal. E.Belchev, S.Hineva: On the minimal hypersurfaces of a locally symmetric manifold. -N.Blasic, N.Bokan, P.Gilkey: The spectral geometry of the Laplacian and the conformal Laplacian for manifolds with boundary. -J.Bolton, W.M.Oxbury, L.Vrancken, L.M. Woodward: Minimal immersions of RP2 into CPn. -W.Cieslak, A. Miernowski, W.Mozgawa: Isoptics of a strictly convex curve. -F.Dillen, L.Vrancken: Generalized Cayley surfaces. -A.Ferrandez, O.J.Garay, P.Lucas: On a certain class of conformally flat Euclidean hypersurfaces. -P.Gauduchon: Self-dual manifolds with non-negative Ricci operator. -B.Hajduk: On the obstruction group toexistence of Riemannian metrics of positive scalar curvature. -U.Hammenstaedt: Compact manifolds with 1/4-pinched negative curvature. -J.Jost, Xiaowei Peng: The geometry of moduli spaces of stable vector bundles over Riemannian surfaces. - O.Kowalski, F.Tricerri: A canonical connection for locally homogeneous Riemannian manifolds. -M.Kozlowski: Some improper affine spheres in A3. -R.Kusner: A maximum principle at infinity and the topology of complete embedded surfaces with constant mean curvature. -Anmin Li: Affine completeness and Euclidean completeness. -U.Lumiste: On submanifolds with parallel higher order fundamental form in Euclidean spaces. -A.Martinez, F.Milan: Convex affine surfaces with constant affine mean curvature. -M.Min-Oo, E.A.Ruh, P.Tondeur: Transversal curvature and tautness for Riemannian foliations. -S.Montiel, A.Ros: Schroedinger operators associated to a holomorphic map. -D.Motreanu: Generic existence of Morse functions on infinite dimensional Riemannian manifolds and applications. -B.Opozda: Some extensions of Radon's theorem.
Proceedings Of The Workshop Contemporary Geometry And Related Topics
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Author : Neda Bokan
language : en
Publisher: World Scientific
Release Date : 2004
Proceedings Of The Workshop Contemporary Geometry And Related Topics written by Neda Bokan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Readership: Researchers in geometry & topology, nonlinear science and dynamical systems.
Contemporary Geometry And Related Topics Proceedings Of The Workshop
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Author : Neda Bokan
language : en
Publisher: World Scientific
Release Date : 2004-03-15
Contemporary Geometry And Related Topics Proceedings Of The Workshop written by Neda Bokan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-15 with Mathematics categories.
This volume covers a broad range of subjects in modern geometry and related branches of mathematics, physics and computer science. Most of the papers show new, interesting results in Riemannian geometry, homotopy theory, theory of Lie groups and Lie algebras, topological analysis, integrable systems, quantum groups, and noncommutative geometry. There are also papers giving overviews of the recent achievements in some special topics, such as the Willmore conjecture, geodesic mappings, Weyl's tube formula, and integrable geodesic flows. This book provides a great chance for interchanging new results and ideas in multidisciplinary studies.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
Geometry And Topology Of Submanifolds Vii Differential Geometry In Honour Of Prof Katsumi Nomizu
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Author : Franki Dillen
language : en
Publisher: World Scientific
Release Date : 1995-05-09
Geometry And Topology Of Submanifolds Vii Differential Geometry In Honour Of Prof Katsumi Nomizu written by Franki Dillen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-05-09 with categories.
This volume on pure and applied differential geometry, includes topics on submanifold theory, affine differential geometry and applications of geometry in engineering sciences. The conference was dedicated to the 70th birthday of Prof Katsumi Nomizu. Papers on the scientific work and life of Katsumi Nomizu are also included.
Tensors And Riemannian Geometry
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Author : Nail H. Ibragimov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-08-31
Tensors And Riemannian Geometry written by Nail H. Ibragimov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-31 with Mathematics categories.
This book is based on the experience of teaching the subject by the author in Russia, France, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics on tensors, Riemannian geometry and geometric approach to partial differential equations. Application of approximate transformation groups to the equations of general relativity in the de Sitter space simplifies the subject significantly.
Geometry And Topology Of Submanifolds X Differential Geometry In Honor Of Professor S S Chern
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Author : Weihuan Chen
language : en
Publisher: World Scientific
Release Date : 2000-11-07
Geometry And Topology Of Submanifolds X Differential Geometry In Honor Of Professor S S Chern written by Weihuan Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-11-07 with Mathematics categories.
Contents:Progress in Affine Differential Geometry — Problem List and Continued Bibliography (T Binder & U Simon)On the Classification of Timelike Bonnet Surfaces (W H Chen & H Z Li)Affine Hyperspheres with Constant Affine Sectional Curvature (F Dillen et al.)Geometric Properties of the Curvature Operator (P Gilkey)On a Question of S S Chern Concerning Minimal Hypersurfaces of Spheres (I Hiric( & L Verstraelen)Parallel Pure Spinors on Pseudo-Riemannian Manifolds (I Kath)Twistorial Construction of Spacelike Surfaces in Lorentzian 4-Manifolds (F Leitner)Nirenberg's Problem in 90's (L Ma)A New Proof of the Homogeneity of Isoparametric Hypersurfaces with (g,m) = (6, 1) (R Miyaoka)Harmonic Maps and Negatively Curved Homogeneous Spaces (S Nishikawa)Biharmonic Morphisms Between Riemannian Manifolds (Y L Ou)Intrinsic Properties of Real Hypersurfaces in Complex Space Forms (P J Ryan)On the Nonexistence of Stable Minimal Submanifolds in Positively Pinched Riemannian Manifolds (Y B Shen & H Q Xu)Geodesic Mappings of the Ellipsoid (K Voss)η-Invariants and the Poincaré-Hopf Index Formula (W Zhang)and other papers Readership: Researchers in differential geometry and topology. Keywords:Conference;Proceedings;Berlin (Germany);Beijing (China);Geometry;Topology;Submanifolds X;Differential Geometry;Dedication