The Lagrangian Gauss Image of a Surface in Euclidean 3-Space
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.
Transactions of the American Mathematical Society, Volume 335, Issue 2, 1993, pages 791-803.
©Transactions of the American Mathematical Society 1993, American Mathematical Society
Kossowski, M. (1993). The Lagrangian Gauss Image of a Surface in Euclidean 3-Space. Transactions of the American Mathematical Society, 335(2), 791-803. https://www.jstor.org/stable/2154405