Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9500440 | Differential Geometry and its Applications | 2005 | 14 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Hajime Ono,