CR submanifolds of maximal CR dimension of complex projective space (Q1270269)

Let \(N\) be a Kähler manifold and \(M\) be a CR submanifold of \(N\) [cf. \textit{A. Bejancu}, `Geometry of CR-submanifolds' (Math. Appl. East Eur. Ser. 23, Kluwer, Dordrecht) (1986; Zbl 0605.53001)]. In the case that the totally real distribution on \(M\) is 1-dimensional, that is, \(M\) has maximal CR dimension, the authors obtain generalizations of some results from the theory of real hypersurfaces of \(N\). As an example, this generalizes a theorem stated by \textit{T. E. Cecil} and \textit{P. J. Ryan} [Trans. Am. Math. Soc. 269, 481-499 (1982; Zbl 0492.53039)] with respect to real hypersurfaces of \(N\) with at most two distinct principal curvatures at each point.