On generic submanifolds of a locally conformal Kähler manifold with parallel canonical structures (Q1805133)

Let \((\widetilde {M}, J)\) be an almost complex manifold with almost complex structure \(J\), and let \(M\) be a submanifold of \(\widetilde {M}\). One denotes \({\mathcal H}_ x = T_ x M \cap J(T_ x M)\) for each point \(x \in M\). If the dimension of \({\mathcal H}_ x\) is constant along \(M\), \(M\) is called a generic submanifold of \((\widetilde {M}, J)\) [see \textit{B. Y. Chen}, Geometry of submanifolds and its applications, Tokyo (1981; Zbl 0474.53050)]. This concept generalizes Bejancu's CR-submanifolds [\textit{A. Bejancu}, Proc. Am. Math. Soc. 69, 135-142 (1978; Zbl 0368.53040)]. In this paper the authors study the generic submanifolds of a locally conformal Kähler manifold [see \textit{I. Vaisman}, Isr. J. Math. 24, 338- 351 (1976; Zbl 0335.53055)]. Using the basic tensors of generic submanifolds, they obtain some interesting results.