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Conformal and related changes of metric on the product of two almost contact metric manifolds. (English) Zbl 0721.53035

From A. Morimoto’s paper [J. Math. Soc. Japan 15, 420-436 (1963; Zbl 0135.221)] it is known that the product of two almost contact manifolds carries a natural almost complex structure whose integrability is equivalent to the normality of both almost contact structures. M. Capursi showed that for the product of two almost contact metric manifolds, the product metric is Kählerian if and only if both factors are cosymplectic [An. Stiint. Univ. Al. I. Cuza Iaşi, N. Ser., Sect. Ia 30, No.1, 75-79 (1984; Zbl 0551.53018)]. The sections 2-3 of the paper deal with some preliminaries on the almost contact manifolds and Kenmotsu manifolds. In the fourth section the authors discuss some properties of trans-Sasakian manifolds proved by J. C. Marrero (that are to be published).
The main results of the paper are given in the last section. The authors consider the conformal and related changes of the metric on the product of two almost contact metric manifolds. They prove that if one factor is Sasakian the other is not but that locally the second factor is of Kenmotsu type.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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