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

Considering n-dimensional real submanifolds M of a complex space form ( M ¯ n + p , g ¯ , J ) which are CR submanifolds of CR dimension 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.