A generalization of Obata’s theorem
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 characterize all compact rank-one symmetric spaces as those Riemannian manifolds (M, g) admitting a real-valued functionu s...
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Veröffentlicht in: | The Journal of geometric analysis 1997, Vol.7 (3), p.357-375 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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 characterize all compact rank-one symmetric spaces as those Riemannian manifolds (M, g) admitting a real-valued functionu such that the hessian ofu has at most two eigenvalues −u and under some mild hypotheses on (M, g). This generalizes a well-known result of Obata which characterizes all round spheres. |
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ISSN: | 1050-6926 1559-002X |
DOI: | 10.1007/BF02921625 |