Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures

Ghosh, Amalendu

Mathematica Bohemica, Tome 141 (2016) no. 3, pp. 315-325

Abstract (VO)

We prove that a connected Riemannian manifold admitting a pair of non-trivial Einstein-Weyl structures $(g, \pm \omega )$ with constant scalar curvature is either Einstein, or the dual field of $\omega $ is Killing. Next, let $(M^n, g)$ be a complete and connected Riemannian manifold of dimension at least $3$ admitting a pair of Einstein-Weyl structures $(g, \pm \omega )$. Then the Einstein-Weyl vector field $E$ (dual to the $1$-form $\omega $) generates an infinitesimal harmonic transformation if and only if $E$ is Killing.

Détail

DOI : 10.21136/MB.2016.0072-14

Classification : 53C15, 53C20, 53C25
Keywords: Weyl manifold; Einstein-Weyl structure; infinitesimal harmonic transformation

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