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Homogeneity of Lorentzian three‐manifolds with recurrent curvature
Author(s) -
GarcíaRío Eduardo,
Gilkey Peter B.,
Nikčević Stana
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200302
Subject(s) - mathematics , homogeneous , curvature , homogeneity (statistics) , ricci curvature , curvature of riemannian manifolds , ricci flat manifold , pure mathematics , mathematical analysis , isometry (riemannian geometry) , scalar curvature , sectional curvature , geometry , combinatorics , statistics
k ‐Curvature homogeneous three‐dimensional Walker metrics are described for k ≤ 2 . This allows a complete description of locally homogeneous three‐dimensional Walker metrics, showing that there exist exactly three isometry classes of such manifolds. As an application one obtains a complete description of all locally homogeneous Lorentzian manifolds with recurrent curvature. Moreover, potential functions are constructed in all the locally homogeneous manifolds resulting in steady gradient Ricci and Cotton solitons.