Cartan-type criterions for constancy of almost Hermitian manifolds

Hakan Mete Taştan

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arXiv · 1311.2509

Cartan-type criterions for constancy of almost Hermitian manifolds

Hakan Mete Taştan

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Abstract

We studied the axiom of anti-invariant 2-spheres and the axiom of co-holomorphic $(2n+1)$-spheres. We proved that a nearly Kählerian manifold satisfying the axiom of anti-invariant 2-spheres is a space of constant holomorphic sectional curvature. We also showed that an almost Hermitian manifold $M$ of dimension $2m\geq6$ satisfying the axiom of co-holomorphic $(2n+1)$-spheres for some $n,$ where $(1\leq n\leq m-1)$, the manifold $M$ has pointwise constant type $α$ if and only if $M$ has pointwise constant anti-holomorphic sectional curvature $α$.

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Hakan Mete Taştan. 2013-11-11. Cartan-type criterions for constancy of almost Hermitian manifolds. https://arxiv.org/abs/1311.2509

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