Orthogonal almost-complex structures of minimal energy

Details Orthogonal almost-complex structures of minimal energy Orthogonal almost-complex structures of minimal energy

2006-09-18

arxiv.org/abs/math/0609511v1

Mathematics

Differential Geometry

Scientific paper

In this article we apply a Bochner type formula to show that on a compact conformally flat riemannian manifold (or half-conformally flat in dimension 4) certain types of orthogonal almost-complex structures, if they exist, give the absolute minimum for the energy functional. We give a few examples when such minimizers exist, and in particular, we prove that the standard almost-complex structure on the round S^6 gives the absolute minimum for the energy. We also discuss the uniqueness of this minimum and the extension of these results to other orthogonal G-structures.

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