Abstract
In this paper, we investigate compact Legendrian submanifolds L in Sasakian manifolds M, which have extremal volume under Legendrian deformations. We call such a submanifold L-minimal Legendrian submanifold. We derive the second variational for-mula for the volume of L under Legendrian deformations in M. Applying this formula, we investigate the stability of L-minimal Legendrian curves in Sasakian space forms, and show the L-instability of L-minimal Legendrian submanifolds in S2n1+1 (1). Moreover, we give a construction of L-minimal Legendrian submanifolds in R2n+1(-3).
Original language | English |
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Pages (from-to) | 523-543 |
Number of pages | 21 |
Journal | Tohoku Mathematical Journal |
Volume | 65 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2013 Dec |
Externally published | Yes |
Keywords
- Legendrian stability
- Legendrian submanifold
- Sasakian manifold
ASJC Scopus subject areas
- Mathematics(all)