Abstract
IfM is a Riemannian manifold, andL is a Lagrangian submanifold ofT * M, the Maslov class ofL has a canonical representative 1-form which we call theMaslov form ofL. We prove that ifL =v * N = conormal bundle of a submanifoldN ofM, its Maslov form vanishes iffN is a minimal submanifold. Particularly, ifM is locally flatv * N is a minimal Lagrangian submanifold ofT * M iffN is a minimal submanifold ofM. This strengthens a result of Harvey and Lawson [H L].
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[HL]Harvey, R., Lawson, H. B.: Calibrated geometries. Acta Math.148, 47–157 (1982).
[V]Vaisman, I.: Symplectic Geometry and Secondary Characteristic Classes. Boston: Birkhäuser. 1987.
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Vaisman, I. Conormal bundles with vanishing Maslov form. Monatshefte für Mathematik 109, 305–310 (1990). https://doi.org/10.1007/BF01320695
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DOI: https://doi.org/10.1007/BF01320695