On extrinsic symmetric CR-structures on the manifolds of complete flags

ALICIA GARCÍA Y CRISTIÁN U. SÁNCHEZ

BEITRAGE R ALGEBRA GEOM

Año: 2004 vol. 45 p. 401 - 414

0138-4821

In the present paper we study extrinsic symmetric CR-structures on the manifolds of complete flags $G_{u}/T$ relating some of them with the inner symmetric spaces $G_{u}/K.$ We show that the maximum possible CR-dimension of any extrinsic symmetric CR-manifold $G_{u}/T$ cannot be larger than half the maximal dimension of the inner symmetric spaces $G_{u}/K.$ The CR-dimension can be this number and in this case, the holomorphic tangent space is the tangent space of $G_{u}/K$ (at some point).