Mathematica Bohemica, Vol. 141, No. 3, pp. 315-325, 2016
Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures
Amalendu Ghosh
Received October 25, 2014. First published June 16, 2016.
Abstract: 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.
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Affiliations: Amalendu Ghosh, Department of Mathematics, Chandernagore College, Strand Road, Chandannagar, District Hooghly, 712 136, West Bengal, India, e-mail: aghosh_70@yahoo.com
