Maria Falcitelli and Anna Maria Pastore: Conformally flat generalized globally framed $f$-space-forms, p.405-417

Abstract:

Conformally flat generalized globally framed $f$-space-forms are studied. In particular, in the case of corank $s>2$, the $\varphi$-sectional curvature $c$, which is pointwise constant, determines the curvature tensor field. The constancy of $c$ implies the flatness of the manifold. If $c$ is not constant, a local classification of the considered spaces is obtained. This allows to produce explicit examples and to discuss the existence of those spaces whose underlying $f$-structure is of a particular type.

Key Words: Conformal flatness, $f$-structure, space-form, generalized space form.

2000 Mathematics Subject Classification: Primary: 53C15,
Secondary: 53C25.

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