Kodai Mathematical Journal

Submanifolds with constant scalar curvature

Jintang Li

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Abstract

Let $M^n$ be a compact submanifold of $S^{n+p}(c)$ with constant scalar curvature. In this paper, we prove that if the squared norm $S$ of the second fundamental form satisfies a certain inequality, then $M^n$ is a totally umbilic or eqality holds and we described all $M^n$ that satisfy this equality.

Article information

Source
Kodai Math. J., Volume 27, Number 3 (2004), 206-213.

Dates
First available in Project Euclid: 28 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1104247346

Digital Object Identifier
doi:10.2996/kmj/1104247346

Mathematical Reviews number (MathSciNet)
MR2100918

Zentralblatt MATH identifier
1110.53045

Citation

Li, Jintang. Submanifolds with constant scalar curvature. Kodai Math. J. 27 (2004), no. 3, 206--213. doi:10.2996/kmj/1104247346. https://projecteuclid.org/euclid.kmj/1104247346


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