A Perspective on Canonical Riemannian Metrics, Catino Giovanni, Mastrolia Paolo

Автор: Vargas Jose G
Название: Differential Geometry for Physicists and Mathematicians
ISBN: 981456639X ISBN-13(EAN): 9789814566391
Издательство: World Scientific Publishing
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Описание: This is a book that the author wishes had been available to him when he was student. It reflects his interest in knowing (like expert mathematicians) the most relevant mathematics for theoretical physics, but in the style of physicists. This means that one is not facing the study of a collection of definitions, remarks, theorems, corollaries, lemmas, etc. but a narrative -- almost like a story being told -- that does not impede sophistication and deep results.It covers differential geometry far beyond what general relativists perceive they need to know. And it introduces readers to other areas of mathematics that are of interest to physicists and mathematicians, but are largely overlooked. Among these is Clifford Algebra and its uses in conjunction with differential forms and moving frames. It opens new research vistas that expand the subject matter.In an appendix on the classical theory of curves and surfaces, the author slashes not only the main proofs of the traditional approach, which uses vector calculus, but even existing treatments that also use differential forms for the same purpose.

Автор: Chen Bang-yen, Ou Ye-lin
Название: Biharmonic Submanifolds And Biharmonic Maps In Riemannian Geometry
ISBN: 9811212376 ISBN-13(EAN): 9789811212376
Издательство: World Scientific Publishing
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Цена: 174240.00 T
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The book aims to present a comprehensive survey on biharmonic submanifolds and maps from the viewpoint of Riemannian geometry. It provides some basic knowledge and tools used in the study of the subject as well as an overall picture of the development of the subject with most up-to-date important results.

Biharmonic submanifolds are submanifolds whose isometric immersions are biharmonic maps, thus biharmonic submanifolds include minimal submanifolds as a subclass. Biharmonic submanifolds also appeared in the study of finite type submanifolds in Euclidean spaces.

Biharmonic maps are maps between Riemannian manifolds that are critical points of the bienergy. They are generalizations of harmonic maps and biharmonic functions which have many important applications and interesting links to many areas of mathematics and theoretical physics.

Since 2000, biharmonic submanifolds and maps have become a vibrant research field with a growing number of researchers around the world, with many interesting results have been obtained.

This book containing basic knowledge, tools for some fundamental problems and a comprehensive survey on the study of biharmonic submanifolds and maps will be greatly beneficial for graduate students and beginning researchers who want to study the subject, as well as researchers who have already been working in the field.

Автор: Epstein
Название: The Geometrical Language of Continuum Mechanics
ISBN: 1107617030 ISBN-13(EAN): 9781107617032
Издательство: Cambridge Academ
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Цена: 49630.00 T
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Описание: Here Epstein deals with modern differential geometry by placing it within the context of its application to the mechanics of deformable media (continuum mechanics). These two disciplines are mutually compatible as one enlightens the understanding of the other. Throughout the book, the mathematical concepts are exemplified by their engineering counterparts.

Автор: Wang Feng Yu
Название: Analysis for Diffusion Processes on Riemannian Manifolds
ISBN: 9814452645 ISBN-13(EAN): 9789814452649
Издательство: World Scientific Publishing
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Описание: Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary.

Автор: Shen Yi-Bing Et Al
Название: Introduction To Modern Finsler Geometry
ISBN: 9814713163 ISBN-13(EAN): 9789814713160
Издательство: World Scientific Publishing
Цена: 42240.00 T
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Описание:

This comprehensive book is an introduction to the basics of Finsler geometry with recent developments in its area. It includes local geometry as well as global geometry of Finsler manifolds.

In Part I, the authors discuss differential manifolds, Finsler metrics, the Chern connection, Riemannian and non-Riemannian quantities. Part II is written for readers who would like to further their studies in Finsler geometry. It covers projective transformations, comparison theorems, fundamental group, minimal immersions, harmonic maps, Einstein metrics, conformal transformations, amongst other related topics. The authors made great efforts to ensure that the contents are accessible to senior undergraduate students, graduate students, mathematicians and scientists.

Автор: Pitts Jon T.
Название: Existence and Regularity of Minimal Surfaces on Riemannian Manifolds. (MN-27):
ISBN: 0691615004 ISBN-13(EAN): 9780691615004
Издательство: Wiley
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Цена: 68640.00 T
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Описание: Mathematical No/ex, 27 Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paper

Автор: Catino Giovanni, Mastrolia Paolo
Название: A Perspective on Canonical Riemannian Metrics
ISBN: 303057184X ISBN-13(EAN): 9783030571849
Издательство: Springer
Цена: 111790.00 T
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Описание: Introduction.- Basic Concepts of Riemannian Geometry.- Commutations & Variations.- The Weyl Tensor.- Curvature Conditions.- Critical Metrics of Riemannian Functionals.- Bochner-Weitzenbцck Formulas and Applications.- Ricci Solitons: Selected Results.- Existence Results of Canonical Metrics on Four Manifolds.- List of Symbols.- References.- Index.

Автор: Javier de Lucas, Cristina Sardon Munoz
Название: A Guide to Lie Systems with Compatible Geometric Structures
ISBN: 1786346974 ISBN-13(EAN): 9781786346971
Издательство: World Scientific Publishing
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The book presents a comprehensive guide to the study of Lie systems from the fundamentals of differential geometry to the development of contemporary research topics. It embraces several basic topics on differential geometry and the study of geometric structures while developing known applications in the theory of Lie systems. The book also includes a brief exploration of the applications of Lie systems to superequations, discrete systems, and partial differential equations.

Offering a complete overview from the topic's foundations to the present, this book is an ideal resource for Physics and Mathematics students, doctoral students and researchers.

Автор: Gromov, Mikhail
Название: Metric structures for riemannian and non-riemannian spaces
ISBN: 0817645829 ISBN-13(EAN): 9780817645823
Издательство: Springer
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Цена: 102480.00 T
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Описание: This book is an English translation of the famous "Green Book" by Lafontaine and Pansu (1979).

Автор: Berestovskii Valerii, Nikonorov Yurii
Название: Riemannian Manifolds and Homogeneous Geodesics
ISBN: 3030566609 ISBN-13(EAN): 9783030566609
Издательство: Springer
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Цена: 130430.00 T
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Описание: Introduction. - 1 Riemannian Manifolds. - 2 Lie Groups and Lie Algebras. - 3 Isometric Flows and Killing Vector Fields on Riemannian Manifolds. - 4 Homogeneous Riemannian Manifolds. - 5 Manifolds With Homogeneous Geodesics. - 6 Generalized Normal Homogeneous ManifoldsWith Intrinsic Metrics. - 7 Clifford-Wolf Homogeneous Riemannian Manifolds. - References. - List of Tables. - Index.

Автор: Mabuchi Toshiki
Название: Test Configurations, Stabilities and Canonical Kдhler Metrics: Complex Geometry by the Energy Method
ISBN: 9811604991 ISBN-13(EAN): 9789811604997
Издательство: Springer
Цена: 60550.00 T
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Описание: The Yau-Tian-Donaldson conjecture for anti-canonical polarization was recently solved affirmatively by Chen-Donaldson-Sun and Tian. In this book, the unsolved cases of the conjecture will be discussed.It will be shown that the problem is closely related to the geometry of moduli spaces of test configurations for polarized algebraic manifolds.

Автор: Esteban Calvino-Louzao, Eduardo Garcia-Rio, Peter Gilkey, JeongHyeong Park, Ramon Vazquez-Lorenzo
Название: Aspects of Differential Geometry III
ISBN: 1627056866 ISBN-13(EAN): 9781627056861
Издательство: Mare Nostrum (Eurospan)
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Цена: 56370.00 T
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Описание: Differential Geometry is a wide field. This volume concentrates on certain aspects that are appropriate for an introduction to the subject. It deals with invariance theory and discusses invariants both of Weyl and not of Weyl type. Homothety homogeneity, local homogeneity, stability theorems, and Walker geometry are discussed. Ricci solitons are presented.