## Illinois Journal of Mathematics

### Obata's theorem for Kähler manifolds

G. Santhanam

#### 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 $\frac{1+u}{2}$.

#### Article information

Source
Illinois J. Math., Volume 51, Number 4 (2007), 1349-1362.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138549

Digital Object Identifier
doi:10.1215/ijm/1258138549

Mathematical Reviews number (MathSciNet)
MR2417432

Zentralblatt MATH identifier
1146.53044

Subjects