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Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry
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Pseudo-riemannian Geometry, Delta-invariants And Applications (Hardcover)
Loot Price: R4,646
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Pseudo-riemannian Geometry, Delta-invariants And Applications (Hardcover)
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Total price: R4,666
Discovery Miles: 46 660
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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.
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