Abstract

PAREDES, MARLIO  and  PINZON, SOFÍA. Rev.colomb.mat. [online]. 2007, vol.41, n.1, pp.23-37. ISSN 0034-7426.

Here we consider the general flag manifold F_θ as a naturally reductive homogeneous space endowed with an U-invariant metric Λ^θ and an invariant almost-complex structure J^θ. The main objective of this work is to explore the riemannian connection associated with the metric Λ^θ in order to calculate some classes of curvatures which should allow us to confirm, in a simple way, that flag manifolds are either not biholomorfically equivalent nor holomorphically isometric to any complex projective space.

Keywords : Homogeneous spaces; flag manifolds; riemannian connection; curvature.

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