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Eigenvalues In Riemannian Geometry

Eigenvalues in Riemannian Geometry PDF
Author: Isaac Chavel
Publisher: Academic Press
ISBN: 9780080874340
Size: 47.23 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 362
View: 2493

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Eigenvalues In Riemannian Geometry

by Isaac Chavel, Eigenvalues In Riemannian Geometry Books available in PDF, EPUB, Mobi Format. Download Eigenvalues In Riemannian Geometry books, The basic goals of the book are: (i) to introduce the subject to those interested in discovering it, (ii) to coherently present a number of basic techniques and results, currently used in the subject, to those working in it, and (iii) to present some of the results that are attractive in their own right, and which lend themselves to a presentation not overburdened with technical machinery.




Riemannian Geometry

Riemannian Geometry PDF
Author: Isaac Chavel
Publisher: Cambridge University Press
ISBN: 1139452576
Size: 39.87 MB
Format: PDF
Category : Mathematics
Languages : en
Pages :
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Riemannian Geometry

by Isaac Chavel, Riemannian Geometry Books available in PDF, EPUB, Mobi Format. Download Riemannian Geometry books, This book provides an introduction to Riemannian geometry, the geometry of curved spaces, for use in a graduate course. Requiring only an understanding of differentiable manifolds, the author covers the introductory ideas of Riemannian geometry followed by a selection of more specialized topics. Also featured are Notes and Exercises for each chapter, to develop and enrich the reader's appreciation of the subject. This second edition, first published in 2006, has a clearer treatment of many topics than the first edition, with new proofs of some theorems and a new chapter on the Riemannian geometry of surfaces. The main themes here are the effect of the curvature on the usual notions of classical Euclidean geometry, and the new notions and ideas motivated by curvature itself. Completely new themes created by curvature include the classical Rauch comparison theorem and its consequences in geometry and topology, and the interaction of microscopic behavior of the geometry with the macroscopic structure of the space.




Riemannian Geometry

Riemannian Geometry PDF
Author: Isaac Chavel
Publisher:
ISBN: 9780521432016
Size: 36.99 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 386
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Riemannian Geometry

by Isaac Chavel, Riemannian Geometry Books available in PDF, EPUB, Mobi Format. Download Riemannian Geometry books, This book provides an introduction to Riemannian geometry, the geometry of curved spaces. Its main theme is the effect of the curvature of these spaces on the usual notions of geometry - distances, areas, and volumes - and on those new notions and ideas motivated by curvature itself. Among the more specialized classical topics in a new setting are volume-comparison theorems, and isoperimetric inequalities - the interplay of curvature with volume of sets and the areas of their boundaries. Completely new themes created by curvature include the interaction of microscopic behavior of the geometry with the macroscopic structure of the space. After considering those topics which would form the core of an introductory course, the book emphasizes more specialized topics, here treated in book form for the first time. Also featured is a nontraditional Notes and Exercises section for each chapter, to develop and enrich the readers appetite for and appreciation of the subject.




Old And New Aspects In Spectral Geometry

Old and New Aspects in Spectral Geometry PDF
Author: M.-E. Craioveanu
Publisher: Springer Science & Business Media
ISBN: 940172475X
Size: 52.25 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 446
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Old And New Aspects In Spectral Geometry

by M.-E. Craioveanu, Old And New Aspects In Spectral Geometry Books available in PDF, EPUB, Mobi Format. Download Old And New Aspects In Spectral Geometry books, It is known that to any Riemannian manifold (M, g ) , with or without boundary, one can associate certain fundamental objects. Among them are the Laplace-Beltrami opera tor and the Hodge-de Rham operators, which are natural [that is, they commute with the isometries of (M,g)], elliptic, self-adjoint second order differential operators acting on the space of real valued smooth functions on M and the spaces of smooth differential forms on M, respectively. If M is closed, the spectrum of each such operator is an infinite divergent sequence of real numbers, each eigenvalue being repeated according to its finite multiplicity. Spectral Geometry is concerned with the spectra of these operators, also the extent to which these spectra determine the geometry of (M, g) and the topology of M. This problem has been translated by several authors (most notably M. Kac). into the col loquial question "Can one hear the shape of a manifold?" because of its analogy with the wave equation. This terminology was inspired from earlier results of H. Weyl. It is known that the above spectra cannot completely determine either the geometry of (M , g) or the topology of M. For instance, there are examples of pairs of closed Riemannian manifolds with the same spectra corresponding to the Laplace-Beltrami operators, but which differ substantially in their geometry and which are even not homotopically equiva lent.




Eigenvalue And Heat Kernel Estimates For The Weighted Laplacian On A Riemannian Manifold

Eigenvalue and Heat Kernel Estimates for the Weighted Laplacian on a Riemannian Manifold PDF
Author: Alberto G. Setti
Publisher:
ISBN:
Size: 20.96 MB
Format: PDF, ePub, Mobi
Category :
Languages : en
Pages : 114
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Eigenvalue And Heat Kernel Estimates For The Weighted Laplacian On A Riemannian Manifold

by Alberto G. Setti, Eigenvalue And Heat Kernel Estimates For The Weighted Laplacian On A Riemannian Manifold Books available in PDF, EPUB, Mobi Format. Download Eigenvalue And Heat Kernel Estimates For The Weighted Laplacian On A Riemannian Manifold books,




Progress In Differential Geometry

Progress in Differential Geometry PDF
Author: Katsuhiro Shiohama
Publisher: Amer Mathematical Society
ISBN:
Size: 77.19 MB
Format: PDF, ePub, Mobi
Category : Geometry, Differential
Languages : en
Pages : 505
View: 6044

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Progress In Differential Geometry

by Katsuhiro Shiohama, Progress In Differential Geometry Books available in PDF, EPUB, Mobi Format. Download Progress In Differential Geometry books, This volume brings together twenty-five research papers and two survey articles on differential geometry and global analysis, areas in which Japanese differential geometers have recently made great progress. Urakawa's paper is a deep and comprehensive survey on recent results and open problems in differential geometry, including Green functions and Liouville type theorems. Yamaguchi's survey deals with the Lie algebra of all infinitesimal automorphisms of a differential system on a manifold and presents basic material on the geometry of differential systems and simple graded Lie algebras over the real or complex numbers. The research articles cover such topics as minimal surfaces, submanifold theory, analysis on manifolds, $L^2$-cohomology theory, and Riemannian geometry. This book will appeal to mathematicians interested in modern differential geometry, as well as to graduate students who are looking for a good overview of some of the main trends in this field.




Dirac Operators In Riemannian Geometry

Dirac Operators in Riemannian Geometry PDF
Author: Thomas Friedrich
Publisher: American Mathematical Soc.
ISBN: 0821820559
Size: 23.65 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 195
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Dirac Operators In Riemannian Geometry

by Thomas Friedrich, Dirac Operators In Riemannian Geometry Books available in PDF, EPUB, Mobi Format. Download Dirac Operators In Riemannian Geometry books, Examines the Dirac operator on Riemannian manifolds, especially its connection with the underlying geometry and topology of the manifold. The presentation includes a review of Clifford algebras, spin groups and the spin representation, as well as a review of spin structures and spin [superscript C] structures. With this foundation established, the Dirac operator is defined and studied, with special attention to the cases of Hermitian manifolds and symmetric spaces. Then, certain analytic properties are established, including self-adjointness and the Fredholm property. An important link between the geometry and the analysis is provided by estimates for the eigenvalues of the Dirac operator in terms of the scalar curvature and the sectional curvature. Considerations of Killing spinors and solutions of the twistor equation on M lead to results about whether M is an Einstein manifold or conformally equivalent to one. Finally, in an appendix, Friedrich gives a concise introduction to the Seiberg-Witten invariants, which are a powerful tool for the study of four-manifolds. There is also an appendix reviewing principal bundles and connections.




Four Topics In Mathematics

Four Topics in Mathematics PDF
Author: Bogoljub Stanković
Publisher: Matematimki Institut
ISBN:
Size: 21.80 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 274
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Four Topics In Mathematics

by Bogoljub Stanković, Four Topics In Mathematics Books available in PDF, EPUB, Mobi Format. Download Four Topics In Mathematics books, This is a collection of four large papers in mathematics decoted to the memory of Professor Hisao Tominaga.