Contact CR-submanifolds with parallel mean curvature vector of a Sasakian space form

U-Hang Ki; Masahiro Kon

ArticleOriginal scientific text

Title

Contact CR-submanifolds with parallel mean curvature vector of a Sasakian space form

Authors ¹, ²

Affiliations

Department of Mathematics, Kyungpook University, Taegu 702-701, Korea
Department of Mathematics, Hirosaki University, Hirosaki 036, Japan

Abstract

The purpose of this paper is to study contact CR-submanifolds with nonvanishing parallel mean curvature vector immersed in a Sasakian space form. In §1 we state general formulas on contact CR-submanifolds of a Sasakian manifold, especially those of a Sasakian space form. §2 is devoted to the study of contact CR-submanifolds with nonvanishing parallel mean curvature vector and parallel f-structure in the normal bundle immersed in a Sasakian space form. Moreover, we suppose that the second fundamental form of a contact CR-submanifold commutes with the f-structure in the tangent bundle, and compute the restricted Laplacian for the second fundamental form in the direction of the mean curvature vector. As applications of this, in §3, we prove our main theorems.

U-H. Ki, M. Kameda and S. Yamaguchi, Compact totally real submanifolds with parallel mean curvature vector field in a Sasakian space form, TRU Math. 23 (1987), 1-15.
U-H. Ki and J. S. Pak, On totally real submanifolds with parallel mean curvature vector of a Sasakian space form, Bull. Korean Math. Soc. 28 (1991), 55-64.
E. Pak, U-H. Ki, J. S. Pak and Y. H. Kim, Generic submanifolds with normal f-structure of an odd-dimensional sphere (I), J. Korean Math. Soc. 20 (1983), 141-161.
K. Yano, On a structure defined by a tensor field f of type (1,1) satisfying $f^{3} + f = 0$ , Tensor (N.S.) 14 (1963), 99-109.
K. Yano and M. Kon, Generic submanifolds of Sasakian manifolds, Kodai Math. J. 3 (1980), 163-196.
K. Yano and M. Kon, CR Submanifolds of Kaehlerian and Sasakian Manifolds, Birkhäuser, Boston 1983.
K. Yano and M. Kon, Structures on Manifolds, World Sci., 1984.
K. Yano and M. Kon, On contact CR submanifolds, J. Korean Math. Soc. 26 (1989), 231-262.

Title

Contact CR-submanifolds with parallel mean curvature vector of a Sasakian space form

Affiliations

Abstract

Bibliography