The Maslov class of some Legendre submanifolds |
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| Affiliation: | 1. Steklov Mathematical Institute, Gubkina 8, 119991 Moscow, Russia;2. Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany;1. ICMAT, Instituto de Ciencias Matemáticas, Campus Cantoblanco UAM, Calle Nicolás Cabrera, 13-15, 28049 Madrid, Spain;2. BCAM, Basque Center of Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Spain |
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| Abstract: | In the paper, by using a differential-geometric machinery, one computes the Maslov class for: a) Legendre curves on S3, with respect to any one of the three classical contact forms of S3; b) Legendre submanifolds for the classical contact structure of the cotangent unit spheres bundles of a Riemannian manifold N. In case b), and if N is flat, the Maslov class is determined by the mean curvature vector, and it vanishes if the Legendre submanifold is minimal. |
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