Sur le th\'eor\`eme de F. Schur pour une vari\'et\'e presque hermitienne
Differential Geometry
2010-09-15 v1
Abstract
Let M be an almost Hermitian manifold of dimension greater or equal to 6. The following theorems are proved: Theorem 1. If M is of pointwise constant {\theta}-holomorphic sectional curvature for a number {\theta} in (0,{\pi}/2) then M is of constant sectional curvature or a K\"ahler manifold of constant holomorphic sectional curvature. Theorem 2. If M is of pointwise constant antiholomorphic sectional curvature and M is an RK-manifold (or AH3-manifold), then M is of constant antiholomorphic sectional curvature.
Keywords
Cite
@article{arxiv.1009.2695,
title = {Sur le th\'eor\`eme de F. Schur pour une vari\'et\'e presque hermitienne},
author = {Ognian Kassabov},
journal= {arXiv preprint arXiv:1009.2695},
year = {2010}
}
Comments
3 pages, MR 84c:53022