Ricci solitons in three-dimensional paracontact geometry
Differential Geometry
2015-12-09 v1
Abstract
We completely describe paracontact metric three-manifolds whose Reeb vector field satisfies the Ricci soliton equation. While contact Riemannian (or Lorentz\-ian) Ricci solitons are necessarily trivial, that is, -contact and Einstein, the paracontact metric case allows nontrivial examples. Both homogeneous and inhomogeneous nontrivial three-dimensional examples are explicitly described. Finally, we correct the main result of [AGAG-D-13-00189], concerning three-dimensional normal paracontact Ricci solitons.
Keywords
Cite
@article{arxiv.1407.3458,
title = {Ricci solitons in three-dimensional paracontact geometry},
author = {Giovanni Calvaruso and Antonella Perrone},
journal= {arXiv preprint arXiv:1407.3458},
year = {2015}
}
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16 pages