Three-dimensional conformally symmetric manifolds

The nonexistence of nontrivial conformally symmetric manifolds in the three-dimensional Riemannian setting is shown. In Lorentzian signature, a complete local classification is obtained. Furthermore, the isometry classes are examined.

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Bibliographic Details
Published inAnnali di matematica pura ed applicata Vol. 193; no. 6; pp. 1661 - 1670
Main Authors Calviño-Louzao, E., García-Río, E., Seoane-Bascoy, J., Vázquez-Lorenzo, R.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2014
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
53B30
53C50
Cotton tensor
Conformally symmetric spaces
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Summary:The nonexistence of nontrivial conformally symmetric manifolds in the three-dimensional Riemannian setting is shown. In Lorentzian signature, a complete local classification is obtained. Furthermore, the isometry classes are examined.
ISSN:0373-3114
1618-1891
DOI:10.1007/s10231-013-0349-3