Curvature of a class of indefinite globally framed $f$-manifolds

Details Curvature of a class of indefinite globally framed $f$-manifolds Curvature of a class of indefinite globally framed $f$-manifolds

2008-03-04

arxiv.org/abs/0803.0427v2

Mathematics

Differential Geometry

17 pages, no figures

Scientific paper

We present a compared analysis of some properties of indefinite almost $\mathcal{S}$-manifolds and indefinite $\mathcal{S}$-manifolds. We give some characterizations in terms of the Levi-Civita connection and of the characteristic vector fields. We study the sectional and ${\phi}$-sectional curvature of indefinite almost $\mathcal{S}$-manifolds and state an expression of the curvature tensor field for the indefinite $\mathcal{S}$-space forms. We analyse the sectional curvature of indefinite $\mathcal{S}$-manifold in which the number of the spacelike characteristic vector fields is equal to that of the timelike characteristic vector fields. Some examples are also described.

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