Overview
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 ?-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 ?-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 ?-invariants and the main extrinsic invariants. Since then many new results concerning these ?-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.
Full Product Details
Author: Bang-yen Chen (Michigan State Univ, Usa)
Publisher: World Scientific Publishing Co Pte Ltd
Imprint: World Scientific Publishing Co Pte Ltd
Dimensions:
Width: 16.80cm
, Height: 3.10cm
, Length: 23.50cm
Weight: 0.871kg
ISBN: 9789814329637
ISBN 10: 9814329630
Pages: 512
Publication Date: 25 March 2011
Audience:
College/higher education
,
Postgraduate, Research & Scholarly
Format: Hardback
Publisher's Status: Active
Availability: Awaiting stock
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Reviews
"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 ""Mathematical Reviews"""
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 Mathematical Reviews
