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.
Citation
Jiancheng Liu. Qiuyan Zhang. "Simons-type inequalities for the compact submanifolds in the space of constant curvature." Kodai Math. J. 30 (3) 344 - 351, October 2007. https://doi.org/10.2996/kmj/1193924938
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