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- W2006498322 abstract "Given a complex Hilbert space H, we study the differential geometry of the manifold M of all projections in V = ℒ(H). Using the algebraic structure of V, a torsionfree affine connection ∇ (that is invariant under the group of automorphisms of V) is defined on every connected component m of M, which in this way becomes a symmetric holomorphic manifold that consists of projections of the same rank r, (0 ≤ r ≤ ∞). We prove that m admits a Riemann structure if and only if m consists of projections that have the same finite rank r or the same finite corank, and in that case ∇ is the Levi-Civita and the Kähler connection of m. Moreover, m turns out to be a totally geodesic Riemann manifold whose geodesics and Riemann distance are computed." @default.
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- W2006498322 date "2002-01-01" @default.
- W2006498322 modified "2023-09-23" @default.
- W2006498322 title "The manifold of finite rank projections in the algebra ℒ(H) of bounded linear operators" @default.
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- W2006498322 doi "https://doi.org/10.1016/s0723-0869(02)80015-9" @default.
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