A dimensional restriction for a class of contact manifolds

Eugenia Loiudice

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arXiv · 1607.07202

A dimensional restriction for a class of contact manifolds

Eugenia Loiudice

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Abstract

In this work we consider a class of contact manifolds $(M,\eta)$ with an associated almost contact metric structure $(\phi, \xi, \eta,g)$. This class contains, for example, nearly cosymplectic manifolds and the manifolds in the class $C_9\oplus C_{10}$ defined by Chinea and Gonzalez. All manifolds in the class considered turn out to have dimension $4n+1$. Under the assumption that the sectional curvature of the horizontal $2$-planes is constant at one point, we obtain that these manifolds must have dimension $5$.

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Eugenia Loiudice. 2016-07-25. A dimensional restriction for a class of contact manifolds. https://arxiv.org/abs/1607.07202

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