FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 2, PAGES 139-146

Almost $C($l)-manifolds

S. V. Kharitonova

Abstract

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In this paper, we study almost $C($l)-manifolds. We obtain necessary and sufficient conditions for an almost contact metric manifold to be an almost $C($l)-manifold. We prove that contact analogs of A. Gray's second and third curvature identities on almost $C($l)-manifolds hold, while a contact analog of A. Gray's first identity holds if and only if the manifold is cosymplectic. It is proved that a conformally flat, almost $C($l)-manifold is a manifold of constant curvature $$l.

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