Codimension reduction and second fundamental form of CR submanifolds in complex space forms

Abstract

Considering n-dimensional real submanifolds M of a complex space form (over(M, -)n + p, over(g, ̄), J) which are CR submanifolds of CR dimension frac(n - m, 2), we study the condition h (F X, Y) + h (X, F Y) = 0 on the structure tensor F naturally induced from the almost complex structure J of the ambient manifold and on the second fundamental form h of submanifolds M. © 2009 Elsevier Inc. All rights reserved.