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

Liu, Jiancheng; Zhang, Qiuyan

Kodai Math. J., Tome 30 (2007) no. 1, p. 344-351 / Harvested from Project Euclid

Résumé

For the compact submanifold M immersed in the standard Euclidean sphere S^n+p or the Euclidean space R^n+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 S^n+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.

Publié le : 2007-10-14
Classification:

@article{1193924938,
     author = {Liu, Jiancheng and Zhang, Qiuyan},
     title = {Simons-type inequalities for the compact submanifolds in the space of constant curvature},
     journal = {Kodai Math. J.},
     volume = {30},
     number = {1},
     year = {2007},
     pages = { 344-351},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1193924938}
}

Liu, Jiancheng; Zhang, Qiuyan. Simons-type inequalities for the compact submanifolds in the space of constant curvature. Kodai Math. J., Tome 30 (2007) no. 1, pp.  344-351. http://gdmltest.u-ga.fr/item/1193924938/