Abstract
We study the concept of curvature homogeneity of type (1,3) introduced by Kowalski and Vanžurová in the context of the standard curvature homogeneity introduced by Singer and studied by many authors. We study a specialization of this property known as homothety \(r\)-curvature homogeneity. We characterize these concepts in terms of model spaces. As the main result, we present two families of three-dimensional Lorentzian metrics on Euclidean space to exhibit various relationships between all introduced concepts of curvature homogeneity and local homogeneity.
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Acknowledgments
The authors would like to thank O. Kowalski for his helpful comments. In addition, this research was jointly funded by National Science Foundation grant DMS-1156608, and by California State University, San Bernardino.
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This research was jointly funded by National Science Foundation grant DMS-1156608, and by California State University, San Bernardino.
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Dunn, C., McDonald, C. Singer invariants and various types of curvature homogeneity. Ann Glob Anal Geom 45, 303–317 (2014). https://doi.org/10.1007/s10455-013-9403-z
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DOI: https://doi.org/10.1007/s10455-013-9403-z