Marlio Paredes and Sofía Pinzón, Curvature on
reductive homogeneous spaces
Abstract
In this work, we consider the general flag manifold $\vb_\Theta$ as a
naturally reductive homogeneous space endows with an
$U$--invariant
metric $\Lambda^{\Theta}$ and an invariant almost-complex structure $J^\Theta$. Our central reference is the section
2 in chapter X of \cite{kn}. The main
objective of this work is to explore the form for the {\em Riemannian connection} associated with the
metric $\Lambda^{\Theta}$ in order to calculate some classes of curvatures
which allow to compare the results that appear in the geometric flag
manifolds with characterizations already
existing (see, for example, \cite{siu}, \cite{eell2}).
If you are interested in
obtaining a copy of this report please contact the authors either via e-mail or
via snail mail. Their postal address is the following:
Escuela de Matem\'aticas
Universidad
Industrial de Santander
Apartado
Aereo 678
Bucaramanga,
Santander, Colombia.
April 04, 2004