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On generic submanifolds of a locally conformal Kähler manifold with parallel canonical structures. (English) Zbl 0824.53057

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 B. Y. Chen, Geometry of submanifolds and its applications, Tokyo (1981; Zbl 0474.53050)]. This concept generalizes Bejancu’s CR-submanifolds [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 I. Vaisman, Isr. J. Math. 24, 338- 351 (1976; Zbl 0335.53055)]. Using the basic tensors of generic submanifolds, they obtain some interesting results.

MSC:

53C40 Global submanifolds
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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