Curvature properties of some three-dimensional almost contact manifolds with \(B\)-metric. II. (English) Zbl 1086.53046

Nakova, Galia; Manev, Mancho

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 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.
For the entire collection see [Zbl 1048.53002].

Reviewer: D. Perrone (Lecce)

MSC:

53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
53D15	Almost contact and almost symplectic manifolds

Citations:

Zbl 0830.53031