Kahler contact distributions

[摘要] Let M(phi, xi, eta, g) be a contact metric manifold and D be its contact distribution. We define a linear connection del on M and relate it with the generalized Tanaka connection introduced by Tanno (1989)[2]. This enables us to give a characterization in terms of del of a strongly pseudo-convex CR-structure on M. Then we prove that del phi = 0 if and only if M is a Sasakian manifold. In this case we call (D, phi, g) a Kahler contact distribution. Finally, we prove that such a (D, phi, g) has constant holomorphic sectional curvature with respect to del if and only M is a Sasakian space form. (C) 2010 Published by Elsevier B.V.

[发布日期] 2010-12-01

[关键词] Contact metric manifold;D-connection;Kahler contact distribution;Sasakian manifold;Sasakian space form