Integral Formulas In Riemannian Geometry

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Integral Formulas In Riemannian Geometry

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Author : Kentaro Yano
language : en
Publisher:
Release Date : 1970

Integral Formulas In Riemannian Geometry written by Kentaro Yano and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Geometry, Riemannian categories.

Integral Formulas In Riemannian Geometry

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Author : Kentaro Yano
language : en
Publisher:
Release Date : 1970

Integral Formulas In Riemannian Geometry written by Kentaro Yano and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.

Riemannian Manifolds

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Author : John M. Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06

Riemannian Manifolds written by John M. Lee 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 2006-04-06 with Mathematics categories.

This book is designed as a textbook for a one-quarter or one-semester graduate course on Riemannian geometry, for students who are familiar with topological and differentiable manifolds. It focuses on developing an intimate acquaintance with the geometric meaning of curvature. In so doing, it introduces and demonstrates the uses of all the main technical tools needed for a careful study of Riemannian manifolds. The author has selected a set of topics that can reasonably be covered in ten to fifteen weeks, instead of making any attempt to provide an encyclopedic treatment of the subject. The book begins with a careful treatment of the machinery of metrics, connections, and geodesics,without which one cannot claim to be doing Riemannian geometry. It then introduces the Riemann curvature tensor, and quickly moves on to submanifold theory in order to give the curvature tensor a concrete quantitative interpretation. From then on, all efforts are bent toward proving the four most fundamental theorems relating curvature and topology: the Gauss–Bonnet theorem (expressing the total curvature of a surface in term so fits topological type), the Cartan–Hadamard theorem (restricting the topology of manifolds of nonpositive curvature), Bonnet’s theorem (giving analogous restrictions on manifolds of strictly positive curvature), and a special case of the Cartan–Ambrose–Hicks theorem (characterizing manifolds of constant curvature). Many other results and techniques might reasonably claim a place in an introductory Riemannian geometry course, but could not be included due to time constraints.

Volterra And Integral Equations Of Vector Functions

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Author : Martin Vath
language : en
Publisher: CRC Press
Release Date : 2000-01-03

Volterra And Integral Equations Of Vector Functions written by Martin Vath and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-03 with Mathematics categories.

"Develops and applies topological and algebraic methods to study abstract Volterra operators and differential equations arising in models for ""real-world"" phenomena in physics, biology, and a host of other disciplines. Presents completely new results that appear in book form for the first time."

Integral Geometry Of Tensor Fields

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Author : V. A. Sharafutdinov
language : en
Publisher: VSP
Release Date : 1994

Integral Geometry Of Tensor Fields written by V. A. Sharafutdinov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Partial Integral Operators And Integro Differential Equations

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Author : Jurgen Appell
language : en
Publisher: CRC Press
Release Date : 2000-02-29

Partial Integral Operators And Integro Differential Equations written by Jurgen Appell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-29 with Mathematics categories.

A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results. The theory and applications of partial integral operators and linea

Parabolic Equations On An Infinite Strip

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Author : Watson
language : en
Publisher: Routledge
Release Date : 2017-10-02

Parabolic Equations On An Infinite Strip written by Watson and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-02 with Mathematics categories.

This book focuses on solutions of second order, linear, parabolic, partial differentialequations on an infinite strip-emphasizing their integral representation, their initialvalues in several senses, and the relations between these.Parabolic Equations on an Infinite Strip provides valuable information-previously unavailable in a single volume-on such topics as semigroup property.. . the Cauchy problem ... Gauss-Weierstrass representation . .. initial limits .. .normal limits and related representation theorems ... hyperplane conditions .. .determination of the initial measure .. . and the maximum principle. It also exploresnew, unpublished results on parabolic limits . . . more general limits ... and solutionssatisfying LP conditions.Requiring only a fundamental knowledge of general analysis and measure theory, thisbook serves as an excellent text for graduate students studying partial differentialequations and harmonic analysis, as well as a useful reference for analysts interested inapplied measure theory, and specialists in partial differential equations.

Conformal Vector Fields Ricci Solitons And Related Topics

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Author : Ramesh Sharma
language : en
Publisher: Springer Nature
Release Date : 2024-01-19

Conformal Vector Fields Ricci Solitons And Related Topics written by Ramesh Sharma and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-19 with Mathematics categories.

This book provides an up-to-date introduction to the theory of manifolds, submanifolds, semi-Riemannian geometry and warped product geometry, and their applications in geometry and physics. It then explores the properties of conformal vector fields and conformal transformations, including their fixed points, essentiality and the Lichnerowicz conjecture. Later chapters focus on the study of conformal vector fields on special Riemannian and Lorentzian manifolds, with a special emphasis on general relativistic spacetimes and the evolution of conformal vector fields in terms of initial data. The book also delves into the realm of Ricci flow and Ricci solitons, starting with motivations and basic results and moving on to more advanced topics within the framework of Riemannian geometry. The main emphasis of the book is on the interplay between conformal vector fields and Ricci solitons, and their applications in contact geometry. The book highlights the fact that Nil-solitons and Sol-solitons naturally arise in the study of Ricci solitons in contact geometry. Finally, the book gives a comprehensive overview of generalized quasi-Einstein structures and Yamabe solitons and their roles in contact geometry. It would serve as a valuable resource for graduate students and researchers in mathematics and physics as well as those interested in the intersection of geometry and physics.

Extrinsic Geometry Of Foliations

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Author : Vladimir Rovenski
language : en
Publisher: Springer Nature
Release Date : 2021-05-22

Extrinsic Geometry Of Foliations written by Vladimir Rovenski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-22 with Mathematics categories.

This book is devoted to geometric problems of foliation theory, in particular those related to extrinsic geometry, modern branch of Riemannian Geometry. The concept of mixed curvature is central to the discussion, and a version of the deep problem of the Ricci curvature for the case of mixed curvature of foliations is examined. The book is divided into five chapters that deal with integral and variation formulas and curvature and dynamics of foliations. Different approaches and methods (local and global, regular and singular) in solving the problems are described using integral and variation formulas, extrinsic geometric flows, generalizations of the Ricci and scalar curvatures, pseudo-Riemannian and metric-affine geometries, and 'computable' Finsler metrics. The book presents the state of the art in geometric and analytical theory of foliations as a continuation of the authors' life-long work in extrinsic geometry. It is designed for newcomers to the field as well as experienced geometers working in Riemannian geometry, foliation theory, differential topology, and a wide range of researchers in differential equations and their applications. It may also be a useful supplement to postgraduate level work and can inspire new interesting topics to explore.

A Mathematician And His Mathematical Work

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Author : Shiing-Shen Chern
language : en
Publisher: World Scientific
Release Date : 1996

A Mathematician And His Mathematical Work written by Shiing-Shen Chern and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.

This volume is about the life and work of Shiing-Shen Chern (1911-), one of the leading mathematicians of this century. The book contains personal accounts by some friends, together with a summary of the mathematical works by Chern himself. Besides a selection of the mathematical papers the book also contains all his papers published after 1988.