2.7. The Second Variation of the Energy Function

The purpose of the present section is to establish the second variation formula for B978012415826900002X/si1096.gif is missing 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
B978012415826900002X/si1102.gif is missing
Here we setB978012415826900002X/si1103.gif is missingand, for anyand any. Letand. Let us assume thatfor any. Ifis a ...

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