2.2. The Energy of a Vector Field
Let (
M,
g) be an
n-dimensional compact oriented Riemannian manifold and
a tangent vector field on
M. Let ∇ be the Levi-Civita connection of (
M,
g). Let
be the regular connection in
induced by ∇ and
the corresponding nonlinear connection on
T(
M). Let
G
s be the Sasaki metric on
T(
M) (associated to the pair
).
a tangent vector field on
M. Let ∇ be the Levi-Civita connection of (
M,
g). Let
be the regular connection in
induced by ∇ and
the corresponding nonlinear connection on
T(
M). Let
G
s be the Sasaki metric on
T(
M) (associated to the pair
).Get Harmonic Vector Fields now with the O’Reilly learning platform.
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