Sur le théorème de F. Schur pour une variété presque hermitienne

Details Sur le théorème de F. Schur pour une variété presque hermitienne Sur le théorème de F. Schur pour une variété presque hermitienne

2010-09-14

arxiv.org/abs/1009.2695v1

C. R. Acad. Bulg. Sci., 35, no. 7, 1982, 905-907

Mathematics

Differential Geometry

3 pages, MR 84c:53022

Scientific paper

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.

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