Volume 55, Issue 3
A Note on Obata Equations on Manifolds with Boundary

Mijia Lai & Huihuang Zhou

J. Math. Study, 55 (2022), pp. 242-253.

Published online: 2022-09

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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.

  • AMS Subject Headings

53A07, 53C24, 53C40

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

laimijia@sjtu.edu.cn (Mijia Lai)

zhouhuihuang@ustc.edu.cn (Huihuang Zhou)

  • BibTex
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  • TXT
@Article{JMS-55-242, author = {Lai , Mijia and Zhou , Huihuang}, title = {A Note on Obata Equations on Manifolds with Boundary}, journal = {Journal of Mathematical Study}, year = {2022}, volume = {55}, number = {3}, pages = {242--253}, 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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v55n3.22.02}, url = {http://global-sci.org/intro/article_detail/jms/20974.html} }
TY - JOUR T1 - A Note on Obata Equations on Manifolds with Boundary AU - Lai , Mijia AU - Zhou , Huihuang JO - Journal of Mathematical Study VL - 3 SP - 242 EP - 253 PY - 2022 DA - 2022/09 SN - 55 DO - http://doi.org/10.4208/jms.v55n3.22.02 UR - https://global-sci.org/intro/article_detail/jms/20974.html KW - Obata type equation, manifolds with boundary, Dupin hypersurfaces. AB -

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.

Mijia Lai & Huihuang Zhou. (2022). A Note on Obata Equations on Manifolds with Boundary. Journal of Mathematical Study. 55 (3). 242-253. doi:10.4208/jms.v55n3.22.02
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