The Tanno-Theorem for Kählerian metrics with arbitrary signature

Details The Tanno-Theorem for Kählerian metrics with arbitrary signature The Tanno-Theorem for Kählerian metrics with arbitrary signature

2010-12-06

arxiv.org/abs/1012.1181v1

Mathematics

Differential Geometry

Scientific paper

Considering a non-constant smooth solution $f$ of the Tanno equation on a closed, connected K\"ahler manifold $(M,g,J)$ with positively definite metric $g$, Tanno showed that the manifold can be finitely covered by $(\mathbb{C}P(n),\mbox{const}\cdot g_{FS})$, where $g_{FS}$ denotes the Fubini-Study metric of constant holomorphic sectional curvature equal to $1$. The goal of this paper is to give a proof of Tannos Theorem for K\"ahler metrics with arbitrary signature.

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