## Kodai Mathematical Journal

### Simons-type inequalities for the compact submanifolds in the space of constant curvature

#### Abstract

For the compact submanifold M immersed in the standard Euclidean sphere Sn+p or the Euclidean space Rn+p, we obtain Simons-type inequalities about the first eigenvalue λ1 and the squared norm of the second fundamental form S respectively. In particular, for the case of the ambient space is Sn+p, we need not the assumption that M is minimal. Following which, we obtain the estimate about the lower bound for S if it is constant respectively.

#### Article information

Source
Kodai Math. J., Volume 30, Number 3 (2007), 344-351.

Dates
First available in Project Euclid: 1 November 2007

https://projecteuclid.org/euclid.kmj/1193924938

Digital Object Identifier
doi:10.2996/kmj/1193924938

Mathematical Reviews number (MathSciNet)
MR2372122

Zentralblatt MATH identifier
1135.53038

#### Citation

Liu, Jiancheng; Zhang, Qiuyan. Simons-type inequalities for the compact submanifolds in the space of constant curvature. Kodai Math. J. 30 (2007), no. 3, 344--351. doi:10.2996/kmj/1193924938. https://projecteuclid.org/euclid.kmj/1193924938