Hypersurfaces in the noncompact Grassmann manifold SU_{2,m}/S(U_2U_m)

Details Hypersurfaces in the noncompact Grassmann manifold SU_{2,m}/S(U_2U_m) Hypersurfaces in the noncompact Grassmann manifold SU_{2,m}/S(U_2U_m)

2009-11-16

arxiv.org/abs/0911.3081v1

Mathematics

Differential Geometry

28 pages

Scientific paper

The Riemannian symmetric space SU_{2,m}/S(U_2U_m) is both Hermitian symmetric and quaternionic Kahler symmetric. Let M be a hypersurface in SU_{2,m}/S(U_2U_m) and denote by TM its tangent bundle. The complex structure of SU_{2,m}/S(U_2U_m) determines a maximal complex subbundle C of TM, and the quaternionic structure of SU_{2,m}/S(U_2U_m) determines a maximal quaternionic subbundle Q of TM. In this article we investigate hypersurfaces in SU_{2,m}/S(U_2U_m) for which C and Q are closely related to the shape of M.

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