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Pseudo Riemannian Geometry Delta Invariants And Applications

Pseudo Riemannian Geometry   delta  invariants and Applications PDF
Author: Bang-yen Chen
Publisher: World Scientific
ISBN: 9814329630
Size: 62.29 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 477
View: 369

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Pseudo Riemannian Geometry Delta Invariants And Applications

by Bang-yen Chen, Pseudo Riemannian Geometry Delta Invariants And Applications Books available in PDF, EPUB, Mobi Format. Download Pseudo Riemannian Geometry Delta Invariants And Applications books, The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory. A number of recent results on pseudo-Riemannian submanifolds are also included.The second part of this book is on ë-invariants, which was introduced in the early 1990s by the author. The famous Nash embedding theorem published in 1956 was aimed for, in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use extrinsic help. However, this hope had not been materialized as pointed out by M Gromov in his 1985 article published in Asterisque. The main reason for this is the lack of control of the extrinsic invariants of the submanifolds by known intrinsic invariants. In order to overcome such difficulties, as well as to provide answers for an open question on minimal immersions, the author introduced in the early 1990s new types of Riemannian invariants, known as ë-invariants, which are very different in nature from the classical Ricci and scalar curvatures. At the same time he was able to establish general optimal relations between ë-invariants and the main extrinsic invariants. Since then many new results concerning these ë-invariants have been obtained by many geometers. The second part of this book is to provide an extensive and comprehensive survey over this very active field of research done during the last two decades.




Pseudo Riemannian Geometry Invariants And Applications

Pseudo Riemannian Geometry     Invariants and Applications PDF
Author: Bang-Yen Chen
Publisher: World Scientific
ISBN: 9814462489
Size: 21.19 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 512
View: 4001

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Pseudo Riemannian Geometry Invariants And Applications

by Bang-Yen Chen, Pseudo Riemannian Geometry Invariants And Applications Books available in PDF, EPUB, Mobi Format. Download Pseudo Riemannian Geometry Invariants And Applications books, The first part of this book provides a self-contained and accessible introduction to the subject in the general setting of pseudo-Riemannian manifolds and their non-degenerate submanifolds, only assuming from the reader some basic knowledge about manifold theory. A number of recent results on pseudo-Riemannian submanifolds are also included. The second part of this book is on δ-invariants, which was introduced in the early 1990s by the author. The famous Nash embedding theorem published in 1956 was aimed for, in the hope that if Riemannian manifolds could be regarded as Riemannian submanifolds, this would then yield the opportunity to use extrinsic help. However, this hope had not been materialized as pointed out by M Gromov in his 1985 article published in Asterisque. The main reason for this is the lack of control of the extrinsic invariants of the submanifolds by known intrinsic invariants. In order to overcome such difficulties, as well as to provide answers for an open question on minimal immersions, the author introduced in the early 1990s new types of Riemannian invariants, known as δ-invariants, which are very different in nature from the classical Ricci and scalar curvatures. At the same time he was able to establish general optimal relations between δ-invariants and the main extrinsic invariants. Since then many new results concerning these δ-invariants have been obtained by many geometers. The second part of this book is to provide an extensive and comprehensive survey over this very active field of research done during the last two decades. Contents:Pseudo-Riemannian ManifoldsBasics on Pseudo-Riemannian SubmanifoldsSpecial Pseudo-Riemannian SubmanifoldsWarped Products and Twisted ProductsRobertson–Walker SpacetimesHodge Theory, Elliptic Differential Operators and Jacobi's Elliptic FunctionsSubmanifolds of Finite TypeTotal Mean CurvaturePseudo-Kähler ManifoldsPara-Kähler ManifoldsPseudo-Riemannian SubmersionsContact Metric Manifolds and Submanifoldsδ-Invariants, Inequalities and Ideal ImmersionsSome Applications of δ-InvariantsApplications to Kähler and Para-Kähler GeometryApplications to Contact GeometryApplications to Affine GeometryApplications to Riemannian SubmersionsNearly Kähler Manifolds and Nearly Kähler S6(1)δ(2)-Ideal Immersions Readership: Graduate and PhD students in differential geometry and related fields; researchers in differential geometry and related fields; theoretical physicists. Keywords:Pseudo-Riemannian Submanifold;δ-Invariants;Spacetimes;Submersion;Lagrangian Submanifolds;Sasakian Manifold;Total Mean Curvature;Submanifold of Finite Type;Affine HypersurfaceKey Features:This is the only book that provides general results on pseudo-Riemannian submanifoldsThis is the only book that provides detailed account on δ-invariantsAt the beginning of each chapter, historical background is providedReviews: “This book gives an extensive and in-depth overview of the theory of pseudo-Riemannian submanifolds and of the delta-invariants. It is written in an accessible and quite self-contained way. Hence it is recommendable for a very broad audience of students and mathematicians interested in the geometry of submanifolds.” Mathematical Reviews “This books is an extensive and comprehensive survey on pseudo–Riemannian submanifolds and δ–invariants as well as their applications. In every aspect, this is an excellent book, invaluable both for learning the topic and a reference. Therefore, it should be strongly recommended for students and mathematicians interested in the geometry of pseudo-Riemannian submanifolds.” Zentralblatt MATH




Clifford Geometric Algebras With Applications To Physics Mathematics And Engineering

Clifford  geometric  Algebras with Applications to Physics  Mathematics  and Engineering PDF
Author: William Eric Baylis
Publisher: Boston : Birkhäuser
ISBN:
Size: 54.29 MB
Format: PDF, Mobi
Category : Algebras de Clifford
Languages : en
Pages : 517
View: 319

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Clifford Geometric Algebras With Applications To Physics Mathematics And Engineering

by William Eric Baylis, Clifford Geometric Algebras With Applications To Physics Mathematics And Engineering Books available in PDF, EPUB, Mobi Format. Download Clifford Geometric Algebras With Applications To Physics Mathematics And Engineering books, This volume offers a comprehensive approach to the theoretical, applied and symbolic computational aspects of the subject. Excellent for self-study, leading experts in the field have written on the of topics mentioned above, using an easy approach with efficient geometric language for non-specialists.




Mathematical Reviews

Mathematical Reviews PDF
Author:
Publisher:
ISBN:
Size: 41.16 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages :
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Mathematical Reviews

by , Mathematical Reviews Books available in PDF, EPUB, Mobi Format. Download Mathematical Reviews books,




Comprehensive Dissertation Index 1861 1972 Mathematics And Statistics

Comprehensive Dissertation Index  1861 1972  Mathematics and statistics PDF
Author: Xerox University Microfilms
Publisher:
ISBN:
Size: 46.23 MB
Format: PDF, Mobi
Category : Dissertations, Academic
Languages : en
Pages :
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Comprehensive Dissertation Index 1861 1972 Mathematics And Statistics

by Xerox University Microfilms, Comprehensive Dissertation Index 1861 1972 Mathematics And Statistics Books available in PDF, EPUB, Mobi Format. Download Comprehensive Dissertation Index 1861 1972 Mathematics And Statistics books,




Physics Briefs

Physics Briefs PDF
Author:
Publisher:
ISBN:
Size: 17.50 MB
Format: PDF, ePub, Mobi
Category : Physics
Languages : en
Pages :
View: 6429

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Physics Briefs

by , Physics Briefs Books available in PDF, EPUB, Mobi Format. Download Physics Briefs books,




Journal Of The Institution Of Electronics And Telecommunication Engineers

Journal of the Institution of Electronics and Telecommunication Engineers PDF
Author: Institution of Electronics and Telecommunication Engineers (India)
Publisher:
ISBN:
Size: 27.40 MB
Format: PDF
Category : Electronics
Languages : en
Pages :
View: 5104

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Journal Of The Institution Of Electronics And Telecommunication Engineers

by Institution of Electronics and Telecommunication Engineers (India), Journal Of The Institution Of Electronics And Telecommunication Engineers Books available in PDF, EPUB, Mobi Format. Download Journal Of The Institution Of Electronics And Telecommunication Engineers books,