Second variation and Legendrian stabilities of minimal Legendrian submanifolds in Sasakian manifolds |
| |
Authors: | Hajime Ono |
| |
Institution: | Department of Mathematics, Tokyo Metropolitan University, Minami-osawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan |
| |
Abstract: | First, we derive a new second variation formula which holds for minimal Legendrian submanifolds in Sasakian manifolds. Using this, we prove that any minimal Legendrian submanifold in an η-Einstein Sasakian manifold with “nonpositive” η-Ricci constant is stable. Next we introduce the notion of the Legendrian stability of minimal Legendrian submanifolds in Sasakian manifolds. Using our second variation formula, we find a general criterion for the Legendrian stability of minimal Legendrian submanifolds in η-Einstein Sasakian manifolds with “positive” η-Ricci constant. |
| |
Keywords: | 53C42 53C25 |
本文献已被 ScienceDirect 等数据库收录! |
|