Geodesic
Complete submanifolds with parallel mean curvature in a sphere
Glasgow mathematical journal, Tome 38 (1996) no. 3, pp. 343-346

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

Let Mn be an n-dimensional manifold immersed in an (n+p)-dimensional unit sphere Sn+p, with mean curvature H and second fundamental form B. We put φ(X, Y) = B(X, Y)–(X, Y)H where X and Y are tangent vector fields on Mn. Assume that the mean curvature is parallel in the normal bundle of Mn in Sn+p. Following Alencar and do Carmo [1] we denote by BH the square of the positive root of 
Vlachos, Theodoros. Complete submanifolds with parallel mean curvature in a sphere. Glasgow mathematical journal, Tome 38 (1996) no. 3, pp. 343-346. doi: 10.1017/S0017089500031773
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[2] 2.Leung, P. F., An estimate on the Ricci curvature of a submanifold and some applications, Proc. Amer. Math. Soc. 114 (1992), 1051–1061. Google Scholar | DOI

[3] 3.Xu, H. W., A rigidity theorem for submanifolds with parallel mean curvature in a sphere, Arch. Math. 61 (1993), 489–496. Google Scholar | DOI

[4] 4.Yau, S. T., Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math. 28 (1975), 201–228. Google Scholar | DOI

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