Geodesic
A Note on Equivariant Embeddings of Grassmannians
Publications de l'Institut Mathématique, _N_S_59 (1996) no. 73, p. 131

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Zbl

Embeddings of Grassmannians realized by identification of a $k$-dimensional subspace of $\Bbb F^m$ with the orthogonal projection onto it are studied. It is shown that such an embedding has parallel second fundamental form and embeds the Grassmannian minimally into a hypersphere of certain Euclidean space of matrices. A result on holomorphic sectional curvature of the complex Grassmannian is also proved.
Classification : 53C40 53C42
Keywords: Riemannian manifold, embedding, Grassmannian, Hermitean matrices, geodesics, holomorphic curvature 
Ivko Dimitrić. A Note on Equivariant Embeddings of Grassmannians. Publications de l'Institut Mathématique, _N_S_59 (1996) no. 73, p. 131 . http://geodesic.mathdoc.fr/item/PIM_1996_N_S_59_73_a10/
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     author = {Ivko Dimitri\'c},
     title = {A {Note} on {Equivariant} {Embeddings} of {Grassmannians}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {131 },
     year = {1996},
     volume = {_N_S_59},
     number = {73},
     zbl = {0965.53038},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1996_N_S_59_73_a10/}
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