Abstract
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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A nuestro querido Domingo Toledo en su cumpleaños 60.
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Bor, G., Hernández-Lamoneda, L. & Salvai, M. Orthogonal almost-complex structures of minimal energy. Geom Dedicata 127, 75–85 (2007). https://doi.org/10.1007/s10711-007-9160-x
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DOI: https://doi.org/10.1007/s10711-007-9160-x