¹Universidad del Turabo, School of Science and Technology, PO Box 3030. PR 00778-3030 Gurabo, Puerto Rico.
E-mail: maparedes@suagm.edu
²Universidad Industrial de Santander, Escuela de Matemáticas, Apartado Aéreo 678 Bucaramanga, Colombia.
E-mail: spinzon@uis.edu.co
^* Partially supported by COLCIENCIAS-COLOMBIA, Grant No. 240-2001.
^** Partially supported by COLCIENCIAS-COLOMBIA, Grant No. 138-2004.

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.

Key words: Homogeneous spaces, flag manifolds, riemannian connection, curvature.

Consideramos aquí la variedad bandera general F_θ como un espacio homogéneo naturalmente reductivo dotado con una métrica U-invariante Λ^θ y una estructura cuasicompleja invariante J^θ. El objetivo principal de este trabajo es explorar la conexión riemanniana asociada con la métrica Λ^θ con el fin de calcular algunas clases de curvaturas las cuales nos permitan confirmar, de manera simple, que las variedades bandera no son bilomórficamente equivalentes ni holomórficamente isométricas a ningún espacio proyectivo complejo.

Palabras clave: Espacios homogéneos, variedades bandera, conección riemanniana, curvatura.

Texto completo disponible en PDF

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