Illinois Journal of Mathematics

Obata's theorem for Kähler manifolds

G. Santhanam

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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

Permanent link to this document
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
Primary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx]
Secondary: 53C22: Geodesics [See also 58E10]

Citation

Santhanam, G. Obata's theorem for Kähler manifolds. Illinois J. Math. 51 (2007), no. 4, 1349--1362. doi:10.1215/ijm/1258138549. https://projecteuclid.org/euclid.ijm/1258138549


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