Grassman manifolds as subsets of Euclidean spaces

Armando Machado; Isabel Salavessa

Grassman manifolds as subsets of Euclidean spaces

Differential Geometry 2021-01-26 v1

Authors: Armando Machado , Isabel Salavessa

Abstract

We consider the Grassman manifold $G(E)$ as the subset of all orthogonal projections of a given Euclidean space $E$ and obtain some explicit formulas concerning the differential geometry of $G(E)$ as a submanifold of $L(E,E)$ endowed with the Hilbert-Schmidt inner product. Most of these formulas can be naturally extended to the infinite dimensional Hilbert space case.

Keywords

grassmann manifold orthogonal projections euclidean space hilbert-schmidt inner product submanifold differential geometry

Cite

@article{arxiv.2101.09731,
  title  = {Grassman manifolds as subsets of Euclidean spaces},
  author = {Armando Machado and Isabel Salavessa},
  journal= {arXiv preprint arXiv:2101.09731},
  year   = {2021}
}

Comments

Latex-reformatted version of the conference article "Grassman manifolds as subsets of Euclidean Spaces", in Differential Geometry, Proc. 5th Int. Colloq., Santiago de Compostela, Spain, 1984, Research Notes in Mathematics, 131, 85-102, Pitman Adv. Pub. Prog., Boston-London-Melbourne (1985); scans of original paper attached as figures

Grassman manifolds as subsets of Euclidean spaces

Abstract

Keywords

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