November 2011
Intermediate to advanced
528 pages
10h 30m
English
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4.2. Three-Dimensional H -Contact Manifolds
The scope of this section is to give a classification of 3-dimensional contact metric manifolds whose Reeb vector field is a harmonic map.
Let (
M
, (
ϕ
,
ξ
,
η
,
g
)) be a 3-dimensional contact metric manifold. For each point
m
∈
M
there is a local orthonormal frame of the form
defined on some open neighborhood
U
of
m
in
M
and consisting of eigenvectors of
h
. Let
. Then
U
1
is an open subset of
M
. Also let
U
2
consist of all
x
∈
M
such that
h
= 0 in a neighborhood of
x
. Then
U
2
is open ...
defined on some open neighborhood
U
of
m
in
M
and consisting of eigenvectors of
h
. Let
. Then
U
1
is an open subset of
M
. Also let
U
2
consist of all
x
∈
M
such that
h
= 0 in a neighborhood of
x
. Then
U
2
is open ...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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