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

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).