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Non-commutative Gauss map. (English) Zbl 0772.53037

The author develops the theory of the Gauss map and supporting functions for hypersurfaces in a compact Lie group. Special care is taken of the case of surfaces in the 3-sphere, where earlier results of Y. Kitagawa [J. Math. Soc. Japan 40, No. 3, 457-476 (1988; Zbl 0642.53059)] are rediscovered. In the general case, the supporting function which describes the difference between right and left Gauss map, generates a family of symplectomorphisms on the orbits of the adjoint representation. A “converse” is discussed.
Reviewer: D.Ferus (Berlin)

MSC:

53C30 Differential geometry of homogeneous manifolds
53B25 Local submanifolds

Citations:

Zbl 0642.53059
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References:

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