Second variational formula and the stability of legendrian minimal submanifolds in sasakian manifolds

Toru Kajigaya

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

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 languageEnglish
Pages (from-to)523-543
Number of pages21
JournalTohoku Mathematical Journal
Volume65
Issue number4
DOIs
Publication statusPublished - 2013 Dec

Keywords

  • Legendrian stability
  • Legendrian submanifold
  • Sasakian manifold

ASJC Scopus subject areas

  • Mathematics(all)

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