The Maslov class of some Legendre submanifolds

I. Vaisman

doi:10.1016/0393-0440(86)90010-0

The Maslov class of some Legendre submanifolds

I. Vaisman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	289-301
Number of pages	13
Journal	Journal of Geometry and Physics
Volume	3
Issue number	3
DOIs	https://doi.org/10.1016/0393-0440(86)90010-0
State	Published - 1986

Keywords

Contact geometry
Legendre submanifolds
Maslov class

ASJC Scopus subject areas

Mathematical Physics
General Physics and Astronomy
Geometry and Topology

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10.1016/0393-0440(86)90010-0

Cite this

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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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AB - 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.

KW - Contact geometry

KW - Legendre submanifolds

KW - Maslov class

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ER -

The Maslov class of some Legendre submanifolds

Abstract

Keywords

ASJC Scopus subject areas

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