Certain Aspects Of Differential Geometry
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Certain Aspects Of Differential Geometry
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Author : Fred Floyd Sayre
language : en
Publisher:
Release Date : 1938
Certain Aspects Of Differential Geometry written by Fred Floyd Sayre and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1938 with Geometry, Differential categories.
Aspects Of Differential Geometry I
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Author : Peter Gilkey
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2015-02-01
Aspects Of Differential Geometry I written by Peter Gilkey and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-01 with Mathematics categories.
Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. In Book I, we focus on preliminaries. Chapter 1 provides an introduction to multivariable calculus and treats the Inverse Function Theorem, Implicit Function Theorem, the theory of the Riemann Integral, and the Change of Variable Theorem. Chapter 2 treats smooth manifolds, the tangent and cotangent bundles, and Stokes' Theorem. Chapter 3 is an introduction to Riemannian geometry. The Levi-Civita connection is presented, geodesics introduced, the Jacobi operator is discussed, and the Gauss-Bonnet Theorem is proved. The material is appropriate for an undergraduate course in the subject. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the Chern-Gauss-Bonnet Theorem for pseudo-Riemannian manifolds with boundary is new.
Manifolds And Differential Geometry
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Author : Jeffrey Marc Lee
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Manifolds And Differential Geometry written by Jeffrey Marc Lee and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Differential geometry began as the study of curves and surfaces using the methods of calculus. This book offers a graduate-level introduction to the tools and structures of modern differential geometry. It includes the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, and de Rham cohomology.
Aspects Of Differential Geometry Iii
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Author : Esteban Calviño-Louzao
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2017-05-25
Aspects Of Differential Geometry Iii written by Esteban Calviño-Louzao and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-25 with Mathematics categories.
Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book III is aimed at the first-year graduate level but is certainly accessible to advanced undergraduates. It deals with invariance theory and discusses invariants both of Weyl and not of Weyl type; the Chern‒Gauss‒Bonnet formula is treated from this point of view. Homothety homogeneity, local homogeneity, stability theorems, and Walker geometry are discussed. Ricci solitons are presented in the contexts of Riemannian, Lorentzian, and affine geometry.
Synthetic Geometry Of Manifolds
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Author : Anders Kock
language : en
Publisher: Cambridge University Press
Release Date : 2010
Synthetic Geometry Of Manifolds written by Anders Kock 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 2010 with Mathematics categories.
This elegant book is sure to become the standard introduction to synthetic differential geometry. It deals with some classical spaces in differential geometry, namely 'prolongation spaces' or neighborhoods of the diagonal. These spaces enable a natural description of some of the basic constructions in local differential geometry and, in fact, form an inviting gateway to differential geometry, and also to some differential-geometric notions that exist in algebraic geometry. The presentation conveys the real strength of this approach to differential geometry. Concepts are clarified, proofs are streamlined, and the focus on infinitesimal spaces motivates the discussion well. Some of the specific differential-geometric theories dealt with are connection theory (notably affine connections), geometric distributions, differential forms, jet bundles, differentiable groupoids, differential operators, Riemannian metrics, and harmonic maps. Ideal for graduate students and researchers wishing to familiarize themselves with the field.
Canadian Journal Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1993-06
Canadian Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-06 with categories.
Some Properties Of Differentiable Varieties And Transformations
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Author : Beniamino Segre
language : en
Publisher: Springer
Release Date : 2012-12-06
Some Properties Of Differentiable Varieties And Transformations written by Beniamino Segre and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present volume contains, together with numerous additions and extensions, the course of lectures which I gave at Pavia (26 September till 5 October 1955) by invitation of the «Centro Internazionale Mate matico Estivo». The treatment has the character of a monograph, and presents various novel features, both in form and in substance; these are indicated in the notes which will be found at the beginning and end of each chapter. Of the nine parts into which the work is divided, the first four are essentially differential in character, the next three deal with algebraic geometry, while the last two are concerned with certain aspects of the theory of differential equations and of correspondences between topo logical varieties. A glance at the index will suffice to give a more exact idea of the range and variety of the contents, whose chief characteristic is that of establishing suggestive and sometimes unforeseen relations between apparently diverse subjects (e. g. differential geometry in the small and also in the large, algebraic geometry, function theory, topo logy, etc.); prominence is given throughout to the geometrical viewpoint, and tedious calculations are as far as possible avoided.
Einstein Hilbert And The Theory Of Gravitation
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Author : Jagdish Mehra
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Einstein Hilbert And The Theory Of Gravitation written by Jagdish Mehra 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 2012-12-06 with Science categories.
Some time ago I published a small piece * dealing with a charming little essay on 'the state of ether in magnetic fields', which the sixteen-year-old Einstein had written while he was awaiting admission to the E. T. H. in Zurich. This paper sought to trace the continuity between Einstein's early interest in electrodynamics and his later work on the special and general relativity theories. On reading this paper, Professor Eugene Wigner asked me whether David Hilbert had not independently discovered the field equations of gravitation. ** His impression from his stay in Gottingen (where Wigner had been Hilbert's assistant for one year in the late nineteen-twenties) was that Hilbert had indeed done so, and he asked me if it was true. I replied to Professor Wigner about Hilbert's contribution to the theory of gravitation. t He kindly encouraged me to expand my account to deal with the intricate and exciting details of the early years in the formulation of the general relativity theory of gravitation. This is what I have sought to do in this study. Albert Einstein created the general relativity theory of gravitation and dominated its development through the rest of his life. His early work on the theory of gravitation, from 1912 to 1916, had the drama of high adventure. It culminated in the establishment of its foundations which have remained unassailed by the theoretical and experimental work of succeeding decades.
Some Aspects Of Differential Geometry
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Author : A. Fialkow
language : en
Publisher:
Release Date : 1934
Some Aspects Of Differential Geometry written by A. Fialkow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1934 with Geometry, Differential categories.
Raoul Bott Collected Papers
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Author : Loring W. Tu
language : en
Publisher: Birkhäuser
Release Date : 2018-03-26
Raoul Bott Collected Papers written by Loring W. Tu and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-26 with Mathematics categories.
This book is the fifth and final volume of Raoul Bott’s Collected Papers. It collects all of Bott’s published articles since 1991 as well as some articles published earlier but missing in the earlier volumes. The volume also contains interviews with Raoul Bott, several of his previously unpublished speeches, commentaries by his collaborators such as Alberto Cattaneo and Jonathan Weitsman on their joint articles with Bott, Michael Atiyah’s obituary of Raoul Bott, Loring Tu’s authorized biography of Raoul Bott, and reminiscences of Raoul Bott by his friends, students, colleagues, and collaborators, among them Stephen Smale, David Mumford, Arthur Jaffe, Shing-Tung Yau, and Loring Tu. The mathematical articles, many inspired by physics, encompass stable vector bundles, knot and manifold invariants, equivariant cohomology, and loop spaces. The nonmathematical contributions give a sense of Bott’s approach to mathematics, style, personality, zest for life, and humanity. In one of the articles, from the vantage point of his later years, Raoul Bott gives a tour-de-force historical account of one of his greatest achievements, the Bott periodicity theorem. A large number of the articles originally appeared in hard-to-find conference proceedings or journals. This volume makes them all easily accessible. It also features a collection of photographs giving a panoramic view of Raoul Bott's life and his interaction with other mathematicians.