Two questions on the exterior geometry of the plücker embeddings of the Grassmann manifolds

Abstract

The Plücker model of the Grassmann manifold G ⁺_p,p+q is considered. The structure of intersections of G ⁺_p,p+q with tangent spaces of G ⁺_p,p+q regarded as subspaces of the ambient exterior algebra is described. An explicit formula for the second fundamental form of G ⁺_2,4 as of a hypersurface in the five-dimensional sphere is given. The level sets of the normal curvature functions for this hypersurface are studied. Bibliography: 3 titles.