LINEAR WEINGARTEN SUBMANIFOLDS IMMERSED IN A SPACE FORM

作者：De Lima Henrique Fernandes^*; Dos Santos Fabio Reis; Da Silva Araujo Jogli Gidel; Lazaro Velasquez Marco Antonio

来源：Kodai Mathematical Journal, 2017, 40(2): 214-228.

DOI：10.2996/kmj/1499846595

• Riemannian space forms
• complete submanifolds
• parallel normalized mean curvature vector field
• linear Weingarten submanifolds
• Clifford torus
• circular and hyperbolic cylinders

In this paper, we deal with complete linear Weingarten submanifolds M-n immersed with parallel normalized mean curvature vector field in a Riemannian space form Q(c)(n+p) of constant sectional curvature c. Under an appropriated restriction on the norm of the traceless part of the second fundamental form, we show that such a submanifold M (n) must be either totally umbilical or isometric to a Clifford torus, if c = 1, a circular cylinder, if c = 0, or a hyperbolic cylinder, if c = -1. We point out that our results are natural generalizations of those ones obtained in [2] and [6].

• 出版日期2017-6