Open Access
Translator Disclaimer
2013 Second variation formula and the stability of Legendrian minimal submanifolds in Sasakian manifolds
Tor Kajigaya
Tohoku Math. J. (2) 65(4): 523-543 (2013). DOI: 10.2748/tmj/1386354294

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 formula 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 $S^{2n+1}(1)$. Moreover, we give a construction of $L$-minimal Legendrian submanifolds in ${\boldsymbol R}^{2n+1}(-3)$.

Citation

Download Citation

Tor Kajigaya. "Second variation formula and the stability of Legendrian minimal submanifolds in Sasakian manifolds." Tohoku Math. J. (2) 65 (4) 523 - 543, 2013. https://doi.org/10.2748/tmj/1386354294

Information

Published: 2013
First available in Project Euclid: 6 December 2013

zbMATH: 1287.53054
MathSciNet: MR3161432
Digital Object Identifier: 10.2748/tmj/1386354294

Subjects:
Primary: 53C42
Secondary: 53C25

Keywords: Legendrian stability , Legendrian submanifold , Sasakian manifold

Rights: Copyright © 2013 Tohoku University

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.65 • No. 4 • 2013
Back to Top