Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The Lagrangian Gauss image of a surface in Euclidean $ 3$-space

Author: Marek Kossowski
Journal: Trans. Amer. Math. Soc. 335 (1993), 791-803
MSC: Primary 53C42; Secondary 57R20, 57R42
MathSciNet review: 1087056
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Abstract: We describe a correspondence between special nonimmersed surfaces in Euclidean $ 3$-space and exact Lagrangian immersions in the cotangent bundle of the unit sphere. This provides several invariants for such nonimmersive maps: the degree of the Gauss map, the Gauss-Maslov class, and the polarization index. The objectives of this paper are to compare these invariants in the cases where the underlying map immerses or fails to immerse and to describe the extend to which these invariants can be prescribed.

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Article copyright: © Copyright 1993 American Mathematical Society