Conormal bundles with vanishing Maslov form

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If M is a Riemannian manifold, and L is a Lagrangian submanifold of T*M, the Maslov class of L has a canonical representative 1-form which we call the Maslov form of L. We prove that if L =v*N = conormal bundle of a submanifold N of M, its Maslov form vanishes iff N is a minimal submanifold. Particularly, if M is locally flat v*N is a minimal Lagrangian submanifold of T*M iff N is a minimal submanifold of M. This strengthens a result of Harvey and Lawson [H L].

Original languageEnglish
Pages (from-to)305-310
Number of pages6
JournalMonatshefte fur Mathematik
Issue number4
StatePublished - Dec 1990

ASJC Scopus subject areas

  • General Mathematics


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