Encyclopaedia of Mathematical Sciences Geometry

Geometry VI

Riemannian Geometry

Authors: Postnikov, M.M.

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About this Textbook

This book treats that part of Riemannian geometry related to more classical topics in a very original, clear and solid style. Before going to Riemannian geometry, the author pre- sents a more general theory of manifolds with a linear con- nection. Having in mind different generalizations of Rieman- nian manifolds, it is clearly stressed which notions and theorems belong to Riemannian geometry and which of them are of a more general nature. Much attention is paid to trans- formation groups of smooth manifolds. Throughout the book, different aspects of symmetric spaces are treated. The author successfully combines the co-ordinate and invariant approaches to differential geometry, which give the reader tools for practical calculations as well as a theoretical understanding of the subject.The book contains a very useful large Appendix on foundations of differentiable manifolds and basic structures on them which makes it self-contained and practically independent from other sources. The results are well presented and useful for students in mathematics and theoretical physics, and for experts in these fields. The book can serve as a textbook for students doing geometry, as well as a reference book for professional mathematicians and physicists.

Reviews

From the reviews of the first edition:

"... The book is .. comprehensive and original enough to be of interest to any professional geometer, but I particularly recommend it to the advanced student, who will find a host of instructive examples, exercises and vistas that few comparable texts offer... "

H.Geiges, Nieuw Archief voor Wiskunde 2002, Vol. 5/3, Issue 4

"... I found the presentation insightful and stimulating. A useful paedagogical device of the text is to make much use of both the index and coordinate-free notations, encouraging flexibility (and pragmatism) in the reader. ... the book should be of use to a wide variaty of readers: the relative beginner, with perhaps an introductory course in differential geometry, will find his horizons greatly expanded in the material for which this prepares him; while the more experienced reader will surely find the more specialised sections informative."

Robert J. Low, Mathematical Reviews, Issue 2002g

"... Insgesamt liegt ein sehr empfehlenswertes Lehrbuch einerseits zur Riemannschen Geometrie und andererseits zur Theorie differenzierbarer Mannigfaltigkeiten vor, wegen der strukturierten Breite der Darstellung sehr gut geeignet sowohl zum Selbststudium für Studierende mathematischer Disziplinen als auch für Dozenten als Grundlage einschlägiger Lehrveranstaltungen."

P. Paukowitsch, Wien (IMN - Internationale Mathematische Nachrichten 190, S. 64-65, 2002)

"M.M. Postnikov has written a well-structured and readable book with a satisfying sense of completeness to it. The reviewer believes this book deserves a place next to the already existing literature on Riemannian geometry, principally as a basis for teaching a course on abstract Riemannian geometry (after an introduction to differentiable manifolds) but also as a reference work." (Eric Boeckx, Zentralblatt MATH, Vol. 993 (18), 2002)


Table of contents (37 chapters)

Table of contents (37 chapters)

Buy this book

eBook 101,14 €
price for India (gross)
  • ISBN 978-3-662-04433-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 119,99 €
price for India (gross)
  • ISBN 978-3-540-41108-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover 119,99 €
price for India (gross)
  • ISBN 978-3-642-07434-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometry VI
Book Subtitle
Riemannian Geometry
Authors
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
91
Copyright
2001
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-04433-9
DOI
10.1007/978-3-662-04433-9
Hardcover ISBN
978-3-540-41108-6
Softcover ISBN
978-3-642-07434-9
Series ISSN
0938-0396
Edition Number
1
Number of Pages
XVIII, 504
Additional Information
Original Russian edition published by Faktorial, Moscow, 1998
Topics