The structure of hypersurfaces with some curvature conditions
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- by Ju Seon Kim PDF
- Proc. Amer. Math. Soc. 125 (1997), 1497-1501 Request permission
Abstract:
Let $M$ be a hypersurface in $\mathbf {R}^{n+1}$, and let $H, R$ denote the mean curvature and the scalar curvature of $M$ respectively. We show that if $M$ is compact and $R>\frac {n-2}{n-1}H^{2}$, then $M$ is diffeomorphic to $S^{n}$. Also we prove that if $M$ is complete, $H$ is constant and $R\geq \frac {n-2}{n-1}H^{2}$, then $M$ is $\mathbf {R}^{n}$ or $S^{n}$ or $S^{n-1}\times \mathbf {R}^{1}$.References
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Additional Information
- Ju Seon Kim
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- Address at time of publication: Department of Mathematics, Myong Ji University, Yongin, 449-728, Seoul, Korea
- Received by editor(s): May 17, 1995
- Received by editor(s) in revised form: November 1, 1995
- Communicated by: Christopher Croke
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1497-1501
- MSC (1991): Primary 53A07; Secondary 53C20
- DOI: https://doi.org/10.1090/S0002-9939-97-03707-6
- MathSciNet review: 1363427