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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics of the Czech Academy of Science
2016-10-01
|
| Series: | Mathematica Bohemica |
| Subjects: | |
| Online Access: | http://mb.math.cas.cz/full/141/3/mb141_3_2.pdf |
| _version_ | 1818293461832433664 |
|---|---|
| author | Amalendu Ghosh |
| author_facet | Amalendu Ghosh |
| author_sort | Amalendu Ghosh |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T03:16:14Z |
| format | Article |
| id | doaj.art-9add0ed8e3064ce8b16b6c2f8d87d33b |
| institution | Directory Open Access Journal |
| issn | 0862-7959 2464-7136 |
| language | English |
| last_indexed | 2024-12-13T03:16:14Z |
| publishDate | 2016-10-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj.art-9add0ed8e3064ce8b16b6c2f8d87d33b2022-12-22T00:01:29ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362016-10-01141331532510.21136/MB.2016.0072-14MB.2016.0072-14Complete Riemannian manifolds admitting a pair of Einstein-Weyl structuresAmalendu GhoshWe 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.http://mb.math.cas.cz/full/141/3/mb141_3_2.pdf Weyl manifold Einstein-Weyl structure infinitesimal harmonic transformation |
| spellingShingle | Amalendu Ghosh Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures Mathematica Bohemica Weyl manifold Einstein-Weyl structure infinitesimal harmonic transformation |
| title | Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures |
| title_full | Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures |
| title_fullStr | Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures |
| title_full_unstemmed | Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures |
| title_short | Complete Riemannian manifolds admitting a pair of Einstein-Weyl structures |
| title_sort | complete riemannian manifolds admitting a pair of einstein weyl structures |
| topic | Weyl manifold Einstein-Weyl structure infinitesimal harmonic transformation |
| url | http://mb.math.cas.cz/full/141/3/mb141_3_2.pdf |
| work_keys_str_mv | AT amalendughosh completeriemannianmanifoldsadmittingapairofeinsteinweylstructures |