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arXiv · 1407.3458

Ricci solitons in three-dimensional paracontact geometry

Giovanni Calvaruso·Antonella Perrone
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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, $K$-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.

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Giovanni Calvaruso, Antonella Perrone. 2014-07-13. Ricci solitons in three-dimensional paracontact geometry. https://doi.org/10.1016/j.geomphys.2015.07.021

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