Grassman manifolds as subsets of Euclidean spaces

Armando Machado; Isabel Salavessa

Grassman manifolds as subsets of Euclidean spaces

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arxiv 2101.09731 v1 pith:YUDY4YFJ submitted 2021-01-24 math.DG

Armando Machado , Isabel Salavessa This is my paper · ORCID

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keywords euclideanformulasgrassmanspacecaseconcerningconsiderdifferential

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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.

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