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 ...Get Harmonic Vector Fields now with the O’Reilly learning platform.
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