November 2011
Intermediate to advanced
528 pages
10h 30m
English
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3.6. The Brito Energy of the Reeb Vector
Let
S
2
n
+1
be the standard odd-dimensional sphere with the canonical metric
g
and let ξ be a Hopf vector field on
S
2
n
+1
. If
η
is the 1-form on
S
2
n
+1
given by
then (
η
,
g
) is a
K
-contact metric structure on
S
2
n
+1
and ξ is the corresponding Reeb vector field (cf. the terminology in
[42]
). In the sequel, we extend Brito's result (cf.
Theorem 3.30
above) to the case of a compact
K
-contact manifold and its associated Reeb vector field. To start with we show that
then (
η
,
g
) is a
K
-contact metric structure on
S
2
n
+1
and ξ is the corresponding Reeb vector field (cf. the terminology in
[42]
). In the sequel, we extend Brito's result (cf.
Theorem 3.30
above) to the case of a compact
K
-contact manifold and its associated Reeb vector field. To start with we show that
Proposition 3.31
Let
be ...
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