3.8. Normal Vector Fields on Principal Orbits
The purpose of this section is to report on a result by G. Nunes & J. Ripoll,
[224]
. Precisely we shall prove the following
Theorem 3.44
[224]
, p. 1091
Let
(
M
,
g
)
be an n-dimensional
(
n
≥ 3)
compact orientable Riemannian manifold and
a compact Lie group acting on M with cohomogeneity one. Let us assume that either G has no singular orbits or each singular orbit of G has dimension
≤
n
− 3.
Let N be a unit normal vector field orthogonal to the principal orbits of G. Then
and N is a critical ...
a compact Lie group acting on M with cohomogeneity one. Let us assume that either G has no singular orbits or each singular orbit of G has dimension
≤
n
− 3.
Let N be a unit normal vector field orthogonal to the principal orbits of G. Then
and N is a critical ...Get Harmonic Vector Fields now with the O’Reilly learning platform.
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