Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The manifold of finite rank projections in the algebra L(H) of bounded
  linear operators   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 $\nabla$ (that is invariant under the group of
automorphisms of V) is defined on every connected component of M, which in this
way becomes a symmetric holomorphic manifold that consists of projections of
the same rank r, (0< r < \infty). 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 $\nabla$ is the Levi-Civita and the
K\"ahler connection of M. Moreover, M turns out to be a totally geodesic
Riemann manifold whose geodesics and Riemann distance are computed.
  Keywords: JBW-algebras, Grassmann manifolds, Riemann manifolds.
  AMS 2000 Subject Classification: 48G20, 72H51.

20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat