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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
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 Fθ as a naturally reductive homogeneous space endowed with an U-invariant metric Λθ and an invariant almost-complex structure Jθ. The main objective of this work is to explore the riemannian connection associated with the metric Λθ 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.