IJPAM: Volume 51, No. 2 (2009)

ON A HYPERSURFACE WITH THE RICCI TENSOR
SATISFYING CERTAIN CONDITIONS

Takashi Ono$^1$, Shizuno Sekiguchi$^2$, Yoshio Matsuyama$^3$
$^{1,2,3}$Department of Mathematics
Chuo University
1-13-27, Kasuga, Bunkyo-ku, Tokyo, 112-8551, JAPAN
e-mail: [email protected]@math.chuo-u.ac.jp


Abstract.The purpose of the present paper is to prove that a hypersurface with the nearly parallel Ricci tensor and a hypersurface with the cyclic parallel Ricci tensor under the assumption with constant mean curvature are locally symmetric.

Received: February 5, 2009

AMS Subject Classification: 53C40, 53B25

Key Words and Phrases: nearly parallel Ricci tensor, cyclic parallel Ricci tensor, parallel Ricci tensor, locally symmetric

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 51
Issue: 2