Geodesic
The gap theorems for some extremal submanifolds in a unit sphere
Communications in Mathematics, Tome 23 (2015) no. 1, pp. 85-93

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Let $M$ be an $n$-dimensional submanifold in the unit sphere $S^{n+p}$, we call $M$ a $k$-extremal submanifold if it is a critical point of the functional $\int _M\rho ^{2k}\,\mathrm{d}v $. In this paper, we can study gap phenomenon for these submanifolds.
Classification : 53C24, 53C40
Keywords: Extremal functional; Mean curvature; Totally umbilical 
@article{COMIM_2015__23_1_a5,
     author = {Wu, Xi Guo and Lan},
     title = {The gap theorems for some extremal submanifolds in a unit sphere},
     journal = {Communications in Mathematics},
     pages = {85--93},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2015},
     mrnumber = {3394079},
     zbl = {1342.53077},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2015__23_1_a5/}
}
TY  - JOUR
AU  - Wu, Xi Guo and Lan
TI  - The gap theorems for some extremal submanifolds in a unit sphere
JO  - Communications in Mathematics
PY  - 2015
SP  - 85
EP  - 93
VL  - 23
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/COMIM_2015__23_1_a5/
LA  - en
ID  - COMIM_2015__23_1_a5
ER  - 
%0 Journal Article
%A Wu, Xi Guo and Lan
%T The gap theorems for some extremal submanifolds in a unit sphere
%J Communications in Mathematics
%D 2015
%P 85-93
%V 23
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/COMIM_2015__23_1_a5/
%G en
%F COMIM_2015__23_1_a5
Wu, Xi Guo and Lan. The gap theorems for some extremal submanifolds in a unit sphere. Communications in Mathematics, Tome 23 (2015) no. 1, pp. 85-93. http://geodesic.mathdoc.fr/item/COMIM_2015__23_1_a5/