Metric Structures In Differential Geometry

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Metric Structures In Differential Geometry

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Author : Gerard Walschap
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-23

Metric Structures In Differential Geometry written by Gerard Walschap and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-23 with Mathematics categories.

This book offers an introduction to the theory of differentiable manifolds and fiber bundles. It examines bundles from the point of view of metric differential geometry: Euclidean bundles, Riemannian connections, curvature, and Chern-Weil theory are discussed, including the Pontrjagin, Euler, and Chern characteristic classes of a vector bundle. These concepts are illustrated in detail for bundles over spheres.

Metric Structures For Riemannian And Non Riemannian Spaces

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Author : Mikhail Gromov
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-25

Metric Structures For Riemannian And Non Riemannian Spaces written by Mikhail Gromov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-25 with Mathematics categories.

This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979). It has been enriched and expanded with new material to reflect recent progress. Additionally, four appendices, by Gromov on Levy's inequality, by Pansu on "quasiconvex" domains, by Katz on systoles of Riemannian manifolds, and by Semmes overviewing analysis on metric spaces with measures, as well as an extensive bibliography and index round out this unique and beautiful book.

Differential Geometric Structures

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Author : Walter A. Poor
language : en
Publisher: Courier Corporation
Release Date : 2015-04-27

Differential Geometric Structures written by Walter A. Poor and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-27 with Mathematics categories.

This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.

Geometric Vector Fields Of Spray And Metric Structures

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Author : Rezso L. Lovas
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2012-06

Geometric Vector Fields Of Spray And Metric Structures written by Rezso L. Lovas and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06 with categories.

Finsler geometry has been a main field of differential geometry in the 20th and 21st century. Its most natural generalizations are spray geometry and the geometry of generalized metric (Riemannian) spaces. This volume contains the author's own results embedded in the solid framework of classical results. Wherever possible, the author uses a modern, index- and coordinate-free apparatus. An Appendix, however, contains the formulations of several geometric objects presented in the text in terms of coordinates as well. The author quotes the most important original sources as well as the treatises recommendable for further reading. The book is reasonably self-contained and gives an overview of the state of the art of spray and metric structures. Thus it may be useful to read it also as a comprehensive yet brief introduction to the field. The prerequisites that are necessary for the reading of this book do not exceed the knowledge of the fundamental notions related to differentiable manifolds, i.e., no previous knowledge of Finsler or spray geometry is required.

The Geometry Of Hessian Structures

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Author : Hirohiko Shima
language : en
Publisher: World Scientific
Release Date : 2007

The Geometry Of Hessian Structures written by Hirohiko Shima and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

The geometry of Hessian structures is a fascinating emerging field of research. It is in particular a very close relative of Knhlerian geometry, and connected with many important pure mathematical branches such as affine differential geometry, homogeneous spaces and cohomology. The theory also finds deep relation to information geometry in applied mathematics. This systematic introduction to the subject first develops the fundamentals of Hessian structures on the basis of a certain pair of a flat connection and a Riemannian metric, and then describes these related fields as applications of the theory."

Differential Geometry

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Author : Jesús A. Alvarez López
language : en
Publisher: World Scientific
Release Date : 2009

Differential Geometry written by Jesús A. Alvarez López and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

A brief portrait of the life and work of Professor Enrique Vidal Abascal / L.A. Cordero -- pt. A. Foliation theory. Characteristic classes for Riemannian foliations / S. Hurder. Non unique-ergodicity of harmonic measures: Smoothing Samuel Petite's examples / B, Deroin. On the uniform simplicity of diffeomorphism groups / T. Tsuboi. On Bennequin's isotopy lemma and Thurston's inequality / Y. Mitsumatsu. On the Julia sets of complex codimension-one transversally holomorphic foliations / T. Asuke. Singular Riemannian foliations on spaces without conjugate points / A. Lytchak. Variational formulae for the total mean curvatures of a codimension-one distribution / V. Rovenski and P. Walczak. On a Weitzenböck-like formula for Riemannian foliations / V. Slesar. Duality and minimality for Riemannian foliations on open manifolds / X.M. Masa. Open problems on foliations -- pt. B. Riemannian geometry. Graphs with prescribed mean curvature / M. Dajczer. Genuine isometric and conformal deformations of submanifolds / R. Tojeiro. Totally geodesic submanifolds in Riemannian symmetric spaces / S. Klein. The orbits of cohomogeneity one actions on complex hyperbolic spaces / J.C. Díaz-Ramos. Rigidity results for geodesic spheres in space forms / J. Roth. Mean curvature flow and Bernstein-Calabi results for spacelike graphs / G. Li and I.M.C. Salavessa. Riemannian geometric realizations for Ricci tensors of generalized algebraic curvature operators / P. Gilkey, S. Nikc̮ević and D. Westerman. Conformally Osserman multiply warped product structures in the Riemannian setting / M. Brozos-Vázquez, M.E. Vázquez-Abal and R. Vázquez-Lorenzo. Riemannian [symbol]-symmetric spaces / M. Goze and E. Remm. Methods for solving the Jacobi equation. Constant osculating rank vs. constant Jacobi osculating rank / T. Arias-Marco. On the reparametrization of affine homogeneous geodesics / Z. Dus̮ek. Conjugate connections and differential equations on infinite dimensional manifolds / M. Aghasi [und weitere]. Totally biharmonic submanifolds / D. Impera and S. Montaldo. The biharmonicity of unit vector fields on the Poincaré half-space H[symbol] / M.K. Markellos. Perspectives on biharmonic maps and submanifolds / A. Balmus. Contact pair structures and associated metrics / G. Bande and A. Hadjar. Paraquaternionic manifolds and mixed 3-structures / S. Ianus and G.E. Vi̮lcu. On topological obstruction of compact positively Ricci curved manifolds / W.-H. Chen. Gray curvature conditions and the Tanaka-Webster connection / R. Mocanu. Riemannian structures on higher order frame bundles from classical linear connections / J. Kurek and W.M. Mikulski. Distributions on the cotangent bundle from torsion-free connections / J. Kurek and W.M. Mikulski. On the geodesics of the rotational surfaces in the Bianchi-Cartan-Vranceanu spaces / P. Piu and M.M. Profir. Cotangent bundles with general natural Kähler structures of quasi-constant holomorphic sectional curvatures / S.L. Druta̮. Polynomial translation Weingarten surfaces in 3-dimensional Euclidean space / M.I. Munteanu and A.I. Nistor. G-structures defined on pseudo-Riemannian manifolds / I. Sánchez-Rodríguez -- List of participants

New Horizons In Differential Geometry And Its Related Fields

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Author : Toshiaki Adachi
language : en
Publisher: World Scientific
Release Date : 2022-04-07

New Horizons In Differential Geometry And Its Related Fields written by Toshiaki Adachi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-07 with Mathematics categories.

This volume presents recent developments in geometric structures on Riemannian manifolds and their discretizations. With chapters written by recognized experts, these discussions focus on contact structures, Kähler structures, fiber bundle structures and Einstein metrics. It also contains works on the geometric approach on coding theory.For researchers and students, this volume forms an invaluable source to learn about these subjects that are not only in the field of differential geometry but also in other wide related areas. It promotes and deepens the study of geometric structures.

Handbook Of Differential Geometry Volume 1

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Author : F.J.E. Dillen
language : en
Publisher: Elsevier
Release Date : 1999-12-16

Handbook Of Differential Geometry Volume 1 written by F.J.E. Dillen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-12-16 with Mathematics categories.

In the series of volumes which together will constitute the Handbook of Differential Geometry a rather complete survey of the field of differential geometry is given. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent). All chapters are written by experts in the area and contain a large bibliography.

Riemannian Metrics Of Constant Mass And Moduli Spaces Of Conformal Structures

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Author : Lutz Habermann
language : en
Publisher: Springer
Release Date : 2007-05-06

Riemannian Metrics Of Constant Mass And Moduli Spaces Of Conformal Structures written by Lutz Habermann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.

This monograph deals with recent questions of conformal geometry. It provides in detail an approach to studying moduli spaces of conformal structures, using a new canonical metric for conformal structures. This book is accessible to readers with basic knowledge in differential geometry and global analysis. It addresses graduates and researchers.

Handbook Of Differential Geometry

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Author : Franki J.E. Dillen
language : en
Publisher: Elsevier
Release Date : 2005-11-29

Handbook Of Differential Geometry written by Franki J.E. Dillen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-29 with Mathematics categories.

In the series of volumes which together will constitute the "Handbook of Differential Geometry" we try to give a rather complete survey of the field of differential geometry. The different chapters will both deal with the basic material of differential geometry and with research results (old and recent).All chapters are written by experts in the area and contain a large bibliography. In this second volume a wide range of areas in the very broad field of differential geometry is discussed, as there are Riemannian geometry, Lorentzian geometry, Finsler geometry, symplectic geometry, contact geometry, complex geometry, Lagrange geometry and the geometry of foliations. Although this does not cover the whole of differential geometry, the reader will be provided with an overview of some its most important areas. . Written by experts and covering recent research. Extensive bibliography. Dealing with a diverse range of areas. Starting from the basics