Geodesic
RIGIDITY THEOREMS FOR HYPERSURFACES WITH CONSTANT SCALAR CURVATURE IN A UNIT SPHERE
Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 235-241

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we give a characterization of Clifford tori and in a unit sphere S n+1 (1). Our results extend the results due to Cheng and Yau [4], and Wang and Xia [11].
DOI : 10.1017/S0017089507003527
Mots-clés : 53C42, 53C20 
WEI, GUOXIN; SUH, YOUNG JIN. RIGIDITY THEOREMS FOR HYPERSURFACES WITH CONSTANT SCALAR CURVATURE IN A UNIT SPHERE. Glasgow mathematical journal, Tome 49 (2007) no. 2, pp. 235-241. doi: 10.1017/S0017089507003527
@article{10_1017_S0017089507003527,
     author = {WEI, GUOXIN and SUH, YOUNG JIN},
     title = {RIGIDITY {THEOREMS} {FOR} {HYPERSURFACES} {WITH} {CONSTANT} {SCALAR} {CURVATURE} {IN} {A} {UNIT} {SPHERE}},
     journal = {Glasgow mathematical journal},
     pages = {235--241},
     year = {2007},
     volume = {49},
     number = {2},
     doi = {10.1017/S0017089507003527},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003527/}
}
TY  - JOUR
AU  - WEI, GUOXIN
AU  - SUH, YOUNG JIN
TI  - RIGIDITY THEOREMS FOR HYPERSURFACES WITH CONSTANT SCALAR CURVATURE IN A UNIT SPHERE
JO  - Glasgow mathematical journal
PY  - 2007
SP  - 235
EP  - 241
VL  - 49
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003527/
DO  - 10.1017/S0017089507003527
ID  - 10_1017_S0017089507003527
ER  - 
%0 Journal Article
%A WEI, GUOXIN
%A SUH, YOUNG JIN
%T RIGIDITY THEOREMS FOR HYPERSURFACES WITH CONSTANT SCALAR CURVATURE IN A UNIT SPHERE
%J Glasgow mathematical journal
%D 2007
%P 235-241
%V 49
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003527/
%R 10.1017/S0017089507003527
%F 10_1017_S0017089507003527

[1] 1. Luis, J. Alias, de Almeida, Sebastião C. and Brasil, Aldir Jr., Hypersurfaces with constant mean curvature and two principal curvatures in S n+1 , An. Acad. Brasil. Cienc. 76 (2004), 489–497. Google Scholar

[2] 2. Cartan, E., Familles de surfaces isoparametriques dans les espaces a courvure constante, Ann. of Math. 17 (1938), 177–191. Google Scholar

[3] 3. Cheng, Q. M., Hypersurfaces in a unit sphere S n+1 (1) with constant scalar curvature, J. London Math. Soc. (2) 64 (2002), 755–768. Google Scholar | DOI

[4] 4. Cheng, S. Y. and Yau, S. T., Hypersurfaces with constant scalar curvature, Math. Ann. 225 (1977), 195–204. Google Scholar

[5] 5. Chern, S. S., Carmo, M. do and Kobayashi, S., Minimal submanifolds of a sphere with second fundamental form of constant length, Functional analysis and related fields (Proc. Conf. for M. Stone, Univ. of Chicago, Chicago 1968), (Spinger-Verlag, 1970), 59–75. Google Scholar

[6] 6. Lawson, H. B., Local rigidity theorems for minimal hypersurfaces, Ann. of Math. 89 (1969), 179–185. Google Scholar | DOI

[7] 7. Li, H., Hypersurfaces with constant scalar curvature in space forms, Math. Ann. 305 (1996), 665–672. Google Scholar

[8] 8. Li, H., Global rigidity theorems of hypersurface, Ark. Mat. 35 (1997), 327–351. Google Scholar | DOI

[9] 9. Otsuki, T., Minimal hypersurfaces in a Riemannian manifold of constant curvature, Amer. J. Math. 92 (1970), 145–173. Google Scholar | DOI

[10] 10. Suh, Y. J. and Yang, H. Y., Kaehler submanifolds with Ricci curvature bounded from below, Michigan Math. J. 53 (2005), 545–552. Google Scholar | DOI

[11] 11. Wang, Q. L. and Xia, C. Y., Rigidity theorems for closed hypersurfaces in space forms, Quart. J. Math. Oxford Ser. (2) 56 (2005), 101–110. Google Scholar

[12] 12. Wei, G., Complete hypersurfaces with constant mean curvature in a unit sphere, Monatsh. Math. 149 (2006), 251–258. Google Scholar

[13] 13. Wei, G., Rigidity theorems for hypersurfaces in a unit sphere, Monatsh. Math. 149 (2006), 343–350. Google Scholar | DOI

Cité par Sources :