2.7. The Second Variation of the Energy Function
The purpose of the present section is to establish the second variation formula for
in the neighborhood of a critical point (i.e., a harmonic vector field).
in the neighborhood of a critical point (i.e., a harmonic vector field).Theorem 2.27 G. Wiegmink,
[309]
Let (
M, g)
be a compact orientable Riemannian manifold and U a tangent vector field on M. Let us consider a smooth 2-
parameter variation of U
and,
for anyand any.
Letand.
Let us assume thatfor any.
Ifis a ...Get Harmonic Vector Fields now with the O’Reilly learning platform.
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