A Note on Obata Equations on Manifolds with Boundary

Mijia Lai, Huihuang Zhou

JOURNAL OF MATHEMATICAL STUDY（2022）

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Abstract

We analyze complete manifolds with boundary which admit solutions to Obata type equations & nabla;(2) f - fg = 0 and & nabla;(2) f = g under various boundary conditions. Given the existence of interior critical points, such manifolds are domains in the hyperbolic space and the Euclidean space respectively.

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Key words

Obata type equation, manifolds with boundary, Dupin hypersurfaces

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