November 2011
Intermediate to advanced
528 pages
10h 30m
English
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Preface
The main object of study in this monograph are
harmonic vector fields on Riemannian manifolds. Let (
M,
g) be a real
n-dimensional Riemannian manifold and
Sn−1 →
S(
M) →
M its tangent sphere bundle. It is a classical fact that
S(
M) may be endowed with a Riemannian metric
(the
Sasaki metric) naturally associated to the Riemannian metric
g on the base manifold (cf. e.g., D.E. Blair, [42]). Therefore any smooth unit tangent vector field
X :
M →
S(
M) may be looked at as a smooth map among the Riemannian manifolds (
M,
g) and (
S(
M),
) so that ...
(the
Sasaki metric) naturally associated to the Riemannian metric
g on the base manifold (cf. e.g., D.E. Blair, [42]). Therefore any smooth unit tangent vector field
X :
M →
S(
M) may be looked at as a smooth map among the Riemannian manifolds (
M,
g) and (
S(
M),
) so that ...Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.