Abstract
It is known that, in a complete Riemannian manifold $(M, g)$, if the Hessian of a real valued function satisfies some suitable conditions, then it restricts the geometry of $(M, g)$. In this paper we give a characterization of a certain class of Kähler manifolds admitting a real valued function $u$ such that the Hessian has two eigenvalues $u$ and $\frac{1+u}{2}$.
Citation
G. Santhanam. "Obata's theorem for Kähler manifolds." Illinois J. Math. 51 (4) 1349 - 1362, Winter 2007. https://doi.org/10.1215/ijm/1258138549
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