Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures

Amalendu Ghosh

Mathematica Bohemica (2016)

  • Volume: 141, Issue: 3, page 315-325
  • ISSN: 0862-7959

Abstract

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We prove that a connected Riemannian manifold admitting a pair of non-trivial Einstein-Weyl structures ( g , ± ω ) with constant scalar curvature is either Einstein, or the dual field of ω 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 , ± ω ) . Then the Einstein-Weyl vector field E (dual to the 1 -form ω ) generates an infinitesimal harmonic transformation if and only if E is Killing.

How to cite

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Ghosh, Amalendu. "Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures." Mathematica Bohemica 141.3 (2016): 315-325. <http://eudml.org/doc/286809>.

@article{Ghosh2016,
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.},
author = {Ghosh, Amalendu},
journal = {Mathematica Bohemica},
keywords = {Weyl manifold; Einstein-Weyl structure; infinitesimal harmonic transformation},
language = {eng},
number = {3},
pages = {315-325},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures},
url = {http://eudml.org/doc/286809},
volume = {141},
year = {2016},
}

TY - JOUR
AU - Ghosh, Amalendu
TI - Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures
JO - Mathematica Bohemica
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 141
IS - 3
SP - 315
EP - 325
AB - 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.
LA - eng
KW - Weyl manifold; Einstein-Weyl structure; infinitesimal harmonic transformation
UR - http://eudml.org/doc/286809
ER -

References

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