Sasakian anti-holomorphic submanifolds of a Kaehler manifold. (Q2711246)

CR-submanifolds of almost Hermitian manifolds have been introduced and studied by \textit{A. Bejancu} [see Geometry of CR-submanifolds, Reidel, Dordrecht (1986; Zbl 0605.53001)]. In this book he also considered the special case of the so-called Sasakian anti-holomorphic submanifolds with flat normal connection of a Kähler manifold. Any Sasakian real hypersurface of a Kähler manifold belongs to this class of submanifolds.NEWLINENEWLINE Based on a result of Sun and Li, the author proves that a Sasakian anti-holomorphic submanifold \(M\) whose holomorphic distribution has dimension not less than 4 is locally a product of a manifold \(M'\) which is homothetic to a Sasakian manifold and a locally Euclidean space \(M''\).NEWLINENEWLINE It should be mentioned that the Preliminaries contain some misprints an incorrect statement and a wrong Weingarten formula.