A Note on Obata Equations on Manifolds with Boundary

Authors

  • Mijia Lai School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
  • Huihuang Zhou School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China

DOI:

https://doi.org/10.4208/jms.v55n3.22.02

Keywords:

Obata type equation, manifolds with boundary, Dupin hypersurfaces.

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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Published

2022-09-01

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Issue

Vol. 55 No. 3 (2022)

Section

Articles

How to Cite

A Note on Obata Equations on Manifolds with Boundary. (2022). Journal of Mathematical Study, 55(3), 242-253. https://doi.org/10.4208/jms.v55n3.22.02