On pinching theorems for compact pseudo-umbilical submanifold

• Autorzy: Mao, J. , Qin, S.
• Języki publikacji: EN

Abstrakty

EN

Consider submanifolds in the nested space. For a compact pseudoumbilical submanifold with parallel mean curvature vector of a Riemannian submanifold with constant curvature immersed in a quasi-constant curvature Riemannian manifold, two sufficient conditions are given to let the pseudo-umbilical submanifold become a totally umbilical submanifold.

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2012
• Tom: Vol. 45, nr 3
• Strony: 645-654
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Mao, J.

autor

Qin, S.

• School Of Mathematics And Computer Science Hubei University Wuhan 430062, People's Republic Of China,

Bibliografia

• [1] S. S. Chern, W. H. Chern, K. S. Lam, Lectures on Differential Geometry, World Scientific Publishing Company, 2006.
• [2] S. T. Yau, Submanifolds with constant mean curvature I-II, Amer. J. Math. 96(2) (1974), 346–366, 97(1) (1975), 76–100.
• [3] J. Mao, G. Li, The compact pseudo-umbilical submanifold with parallel mean curvature vector in the Riemannian manifold with constant curvature, Journal of Hubei University (Natural Science) 31(4) (2009), 339–342 (in Chinese).
• [4] J. Mao, L. Zhang, Pinching theorems for pseudo-umbilical submanifold, Journal of Jianghan University (Natural Science) 36(3) (2008), 8–10 (in Chinese).