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Curvature properties of some three-dimensional almost contact manifolds with $B$-metric. II. (English) Zbl 1086.53046
Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 5th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 5--12, 2003. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-8-7/pbk). 169-177 (2004).
A $B$-metric on a $(2n+1)$-dimensional almost contact manifold $(M,\xi,\eta,\phi)$ is a metric $g$ such that $g(\phi X,\phi Y)=-g(X,Y)+\eta(X)\eta(Y)$. $g$ is an indefinite metric of signature $(n, n+1)$. A decomposition of the class of almost contact manifolds with $B$-metric was given by {\it G. Gachev, V. Mihova} and {\it K. Gribachev} [Math. Balk., New Ser. 7, No. 3--4, 264--276 (1993; Zbl 0830.53031)], where eleven basic classes are defined. In this paper the authors study curvature properties and geometric characteristics of a 3-dimensional almost contact manifold with a $B$-metric belonging to two main classes. For the entire collection see [Zbl 1048.53002].

53C15Differential geometric structures on manifolds
53D15Almost contact and almost symplectic manifolds
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