Geodesic
Two questions in the exterior geometry of Plucker embeddings for Grassmannian manifolds
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 2, Tome 246 (1997), pp. 5-12

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For the Plucker model of the Grassmannian manifold $G^+_{p,p+q}$ a structure of the intersection of the manifold with its own tangent space at an arbitrary point considered as a subspace of the exterior algebra is described. A direct formula for the second main form of the manifold $G^+_{2,4}$ as a hypersurface in a five-dimensional sphere is given. Sets of the constancy for the function of the normal curvature for this hypersurface are studied. 
@article{ZNSL_1997_246_a0,
     author = {A. N. Glushakov},
     title = {Two questions in the exterior geometry of {Plucker} embeddings for {Grassmannian} manifolds},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--12},
     publisher = {mathdoc},
     volume = {246},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_246_a0/}
}
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A. N. Glushakov. Two questions in the exterior geometry of Plucker embeddings for Grassmannian manifolds. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 2, Tome 246 (1997), pp. 5-12. http://geodesic.mathdoc.fr/item/ZNSL_1997_246_a0/