The projective rank of a Hermitian symmetric space: a geometric approach and consequences |
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Authors: | Cristián U Sánchez Ana Giunta |
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Institution: | (1) Fa.M.A.F. Universidad Nacional de Córdoba, Ciudad Universitaria, 5000, Córdoba, Argentina , AR;(2) Departamento de Matemática, Facultad de Ciencias Fis. Mat. y Nat., Universidad Nacional de San Luis Chacabuco y Pedernera, 5700, San Luis, Argentina , AR |
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Abstract: | The “Projective Rank” of a compact connected irreducible Hermitian symmetric space M has been defined as the maximal complex dimension of the compact totally geodesic complex submanifolds having positive holomorphic bisectional curvature with the induced K?hler metric. We present a geometric way to compute this
invariant for the space M based on ideas developed in 1], 13] and 14]. As a consequence we obtain the following inequality relating the Projective Rank, Pr(M), the usual rank,rk(M), and the 2-number # (which is known to be equal to the Euler-Poincare characteristic in these spaces).
Received: 6 June 2000 / Published online: 1 February 2002 |
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Keywords: | Mathematics Subject Classification (1991): 53C35 53C55 |
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