L<sub>n/2</sub>-pinching theorem for submanifolds in a sphere

Xu, Huiqun

L_n/2-pinching theorem for submanifolds in a sphere

Xu, Huiqun

Kodai Math. J., Tome 30 (2007) no. 1, p. 246-251 / Harvested from Project Euclid

Résumé

Let Mⁿ (n ≥ 2) be a n-dimensional oriented closed submanifolds with parallel mean curvature in S^{n + p} (1), denote by S, the norm square of the second fundamental form of M. H is the constant mean curvature of M. We prove that if ∫_M S^n/2 ≤ A(n), where A(n) is a positive universal constant, then M must be a totally umbilical hypersurface in the sphere S^{n + 1}.

Publié le : 2007-06-14
Classification:

@article{1183475515,
     author = {Xu, Huiqun},
     title = {L<sub>n/2</sub>-pinching theorem for submanifolds in a sphere},
     journal = {Kodai Math. J.},
     volume = {30},
     number = {1},
     year = {2007},
     pages = { 246-251},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183475515}
}

Xu, Huiqun. L_n/2-pinching theorem for submanifolds in a sphere. Kodai Math. J., Tome 30 (2007) no. 1, pp.  246-251. http://gdmltest.u-ga.fr/item/1183475515/