International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 11, Pages 651-664
doi:10.1155/S0161171202012267

Families of (1,2)-symplectic metrics on full flag manifolds

Marlio Paredes1,2

1Departamento de Matemática, IMECC-UNICAMP, Campinas 13083-970, SP, Brazil
2Escuela de Matemáticas, Universidad Industrial de Santander, Bucaramanga A.A. 678, Colombia

Received 3 March 2001; Revised 9 July 2001

Copyright © 2002 Marlio Paredes. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We obtain new families of (1,2)-symplectic invariant metrics on the full complex flag manifolds F(n). For n≥5, we characterize n−3 different n-dimensional families of (1,2)-symplectic invariant metrics on F(n). Each of these families corresponds to a different class of nonintegrable invariant almost complex structures on F(n).