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arXiv · 2005.08643

Metric $f$-contact manifolds satisfying the $(\kappa,\mu)$-nullity condition

Alfonso Carriazo·Luis M. Fernández·Eugenia Loiudice
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Abstract

We prove that if the $f$-sectional curvature at any point $p$ of a $(2n+s)$-dimensional $f$-$(\kappa,\mu)$ manifold with $n>1$ is independent of the $f$-section at $p$, then it is constant on the manifold. Moreover, we also prove that an $f$-$(\kappa,\mu)$ manifold which is not an $S$-manifold is of constant $f$-sectional curvature if and only if $\mu=\kappa+1$ and we give an explicit expression for the curvature tensor field. Finally, we present some examples.

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Alfonso Carriazo, Luis M. Fernández, Eugenia Loiudice. 2020-05-18. Metric $f$-contact manifolds satisfying the $(\kappa,\mu)$-nullity condition. https://arxiv.org/abs/2005.08643

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