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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,ξ,η,φ) is a metric g such that g(φX,φY)=-g(X,Y)+η(X)η(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 G. Gachev, V. Mihova and 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.
MSC:
53C15Differential geometric structures on manifolds
53D15Almost contact and almost symplectic manifolds