Conformally invariant tensors on almost contact manifolds with \(B\)- metric. (English) Zbl 0833.53034

Manev, Mancho; Gribachev, Kostadin

Serdica 20, No. 2, 133-147 (1994).

Let \(M\) be an almost contact manifold [D. E. Blair, Contact manifolds in Riemannian geometry, Lect. Notes Math. 509 (Springer 1976; Zbl 0319.53026)] with a \(B\)-metric \(g\), i.e. a semi-Riemannian metric of signature \((n+1, n)\) which is skew compatible. A classification of such manifolds is given in [G. Ganchev, V. Mihova and K. Gribachev, Serdica 19, No. 4, 287-299 (1993)].
A canonical connection of these classes is introduced with respect to which the structure tensors are covariantly constant. Conformally invariant tensors with respect to groups of contact conformal transformations of the considered classes are found. Finally the geometric interpretation of the Bochner curvature tensor is given.

Reviewer: C.-L.Bejan (Iaşi)

MSC:

53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25	Special Riemannian manifolds (Einstein, Sasakian, etc.)
53C50	Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics

Keywords:

conformally invariant tensors; contact conformal transformations; Bochner tensor; almost contact manifold; \(B\)-metric

Citations:

Zbl 0319.53026