Relatório de Pesquisa 17/2004

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