Reduction of the codimension of totally real submanifolds of a complex space form (Q1101701)

The authors prove the following result. Let \(\bar M\) be a complex space form and M an n-dimensional totally real submanifold of \(\bar M.\) If the induced f-structure in the normal bundle is parallel, then there exists a totally geodesic complex space form of complex dimension n of \(\bar M\) in which M is totally real. \{Reviewer's remark: The same result can be found in \textit{M. Hendrickx} and \textit{L. Verstraelen}, Soochow J. Math. 4, 55-61 (1978; Zbl 0406.53051).\}