Geodesic
LINEAR WEINGARTEN HYPERSURFACES IN A REAL SPACE FORM
Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 635-648

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

In this paper, we investigate linear Weingarten hypersurfaces with two distinct principal curvatures in a real space form Mn+1(c), we obtain two rigidity results and give some characterization of the Riemannian product Sk(a) × Sn−k(), 1 ≤ k ≤ n − 1 in Mn+1(c)(c = 1), the Riemannian product Rk × Sn−k(a), 1 ≤ k ≤ n −1 in Mn+1(c)(c = 0) and the Riemannian product Hk(tanh2 ρ−1) × Sn−k(coth2 ρ−1), 1 ≤ k ≤ n −1 in Mn+1(c)(c = −1).
DOI : 10.1017/S0017089510000480
Mots-clés : 53C42, 53A10 
SHU, SHICHANG. LINEAR WEINGARTEN HYPERSURFACES IN A REAL SPACE FORM. Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 635-648. doi: 10.1017/S0017089510000480
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     title = {LINEAR {WEINGARTEN} {HYPERSURFACES} {IN} {A} {REAL} {SPACE} {FORM}},
     journal = {Glasgow mathematical journal},
     pages = {635--648},
     year = {2010},
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     number = {3},
     doi = {10.1017/S0017089510000480},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000480/}
}
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[1] 1.Cartan, E., Sur des familles remarquables d'hypersurfaces isoparamétriques dans les espaces sphériques, Math. Z. 45 (1939), 335–367. Google Scholar | DOI

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

[3] 3.Cheng, Q. M., Hypersurfaces in a unit sphere S n+1(1) with constant scalar curvature, J. Lond. Math. Soc. 64 (2001), 755–768. Google Scholar | DOI

[4] 4.Cheng, Q. M., Complete hypersurfaces in a Euclidean space R n+1 with constant scalar curvature, Indiana Univ. Math. J. 51 (2002), 53–68. Google Scholar | DOI

[5] 5.Hu, Z. and Zhai, S., Hypersurfaces of the hyperbolic space with constant scalar curvature, Results Math. 48 (2005), 65–88. Google Scholar | DOI

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

[7] 7.Li, H., Suh, Y. J. and Wei, G., Linear Weingarten hypersurfaces in a unit sphere, Bull. Korean Math. Soc. 46 (2009), 321–329. Google Scholar | DOI

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

[9] 9.Shu, S. and Yi Han, A., Hypersurfaces in a hyperbolic space with constant k-th mean curvature, Bull. Math. Soc. Sci. Math. Roumanie 52 (100) (2009), 65C78. Google Scholar

[10] 10.Shu, S. and Yi Han, A., Nonnegative sectional curvature hypersurfaces in a real space form, Math. Notes 86 (2009), 729–743. Google Scholar | DOI

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

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