PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 59(73), pp. 131--137 (1996)
A note on equivariant embeddings of Grassmannians
Ivko Dimitri\'cMathematics Department, Pennsylvania State University -- Fayette P.O. Box 519, Uniontown, PA 15401, USA
Abstract: 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.
Keywords: Riemannian manifold, embedding, Grassmannian, Hermitean matrices, geodesics, holomorphic curvature
Classification (MSC2000): 53C40; 53C42
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© 2001 Mathematical Institute of the Serbian Academy of Science and Arts