Reznikov, A. G. Non-commutative Gauss map. (English) Zbl 0772.53037 Compos. Math. 83, No. 1, 53-68 (1992). 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) Cited in 3 Documents MSC: 53C30 Differential geometry of homogeneous manifolds 53B25 Local submanifolds Keywords:flat surfaces; Weyl’s tube; hypersurfaces; adjoint representation Citations:Zbl 0642.53059 PDFBibTeX XMLCite \textit{A. G. Reznikov}, Compos. Math. 83, No. 1, 53--68 (1992; Zbl 0772.53037) Full Text: Numdam EuDML References: [1] V.I. Arnold : The mathematical methods of the classical mechanics . Nauka. [2] A. Besse : Manifolds, all of whose geodesics are closed . Springer-Verlag. · Zbl 0387.53010 [3] Yu. D. Burago V.A. Zalgaller : Geometric inequalities . Springer-Verlag. · Zbl 0633.53002 [4] D. Bennequin : Enlacements et equations de Pfaff , Asterisque 107-108 (1982), 87-102. · Zbl 0573.58022 [5] A.G. Reznikov : Blaschke manifolds of the type of projective planes , Funct. Anal. and its Appl. 19(2) (1985), 88-89. · Zbl 0588.53036 · doi:10.1007/BF01078403 [6] A.G. Reznikov : Totally geodesic fibrations of Lie groups, Differentsialnaya geometriya mnogoobrazii figur , No. 16, 67-70, Kaliningrad, 1985 (Russian). · Zbl 0672.53042 [7] Y. Kitagawa : Periodicity of the asymptotic curves on flat tori in S3 , J. Math. Soc. Japan 40 (3) (1988), 457-476. · Zbl 0642.53059 · doi:10.2969/jmsj/04030457 [8] F. Zak : The structure of the Gauss maps , Funct. Anal and Appl. 21 (1) (1987), 39-50. · Zbl 0623.14026 · doi:10.1007/BF01077983 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.