November 2011
Intermediate to advanced
528 pages
10h 30m
English
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3.7. Vector Fields with Singularities
One of the conclusions of the previous section is that Hopf vector fields on
S
n
with
n
= 2
m
+ 1 aren't minima of the Dirichlet energy functional
. The remaining problem is of course to compute
and investigate whether this is achieved for some vector field perhaps allowed to possess (a finite number of) singular points. For instance, radial vector fields on
S
n
are examples of unit vector fields with only isolated singularities.
. The remaining problem is of course to compute
and investigate whether this is achieved for some vector field perhaps allowed to possess (a finite number of) singular points. For instance, radial vector fields on
S
n
are examples of unit vector fields with only isolated singularities.
3.7.1. Geodesic Distance
Let (
M
,
g
) be a Riemannian manifold and
p
∈
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