Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures
We prove that a connected Riemannian manifold admitting a pair of non-trivial Einstein-Weyl structures $(g, \pmømega)$ with constant scalar curvature is either Einstein, or the dual field of $ømega$ is Killing. Next, let $(M^n, g)$ be a complete and connected Riemannian manifold of dimension at leas...
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2016-10-01
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| Series: | Mathematica Bohemica |
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| Online Access: | http://mb.math.cas.cz/full/141/3/mb141_3_2.pdf |
| Summary: | We prove that a connected Riemannian manifold admitting a pair of non-trivial Einstein-Weyl structures $(g, \pmømega)$ with constant scalar curvature is either Einstein, or the dual field of $ømega$ 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 $(g, \pmømega)$. Then the Einstein-Weyl vector field $E$ (dual to the $1$-form $ømega$) generates an infinitesimal harmonic transformation if and only if $E$ is Killing. |
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| ISSN: | 0862-7959 2464-7136 |