Letizia Brunetti and Anna Maria Pastore: Curvature of a class of indefinite globally framed $f$-manifolds, p.183-204

Abstract:

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 ${\varphi}$-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.

Key Words: Semi-Riemannian manifolds, indefinite metrics, $f$-structures, sectional curvature, $\varphi$-sectional curvature.

2000 Mathematics Subject Classification: Primary: 53C50,
Secondary: 53C15, 53D10

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