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Second order parallel tensors and Ricci solitons in \(3\)-dimensional normal paracontact geometry

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Abstract

The aim of this paper is to study two problems in the framework of paracontact geometry of dimension \(3\), namely, the class of parallel symmetric tensor fields of \((0, 2)\)-type and possible Lorentz Ricci solitons. We search for two types of Ricci solitons: the first when its potential vector field is exactly the characteristic vector field \(\xi \) of the paracontact structure and the second when the potential vector field is a paracontact-holomorphic one. For the former case we find all variants of Ricci solitons, expanding, steady and shrinking, and the fact that \(\xi \) is a conformal Killing vector field. A class of examples is completely discussed.

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Acknowledgments

The authors warmly express their deep thanks to Professor Stefan Ivanov for very useful remarks and helpful comments concerning this paper.

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Authors and Affiliations

  1. Seminarul Matematic “Al. Myller”, University “Al. I. Cuza”, 700506 , Iaşi, Romania

    Cornelia Livia Bejan

  2. Faculty of Mathematics, University “Al. I. Cuza”, 700506 , Iaşi, Romania

    Mircea Crasmareanu

Authors
  1. Cornelia Livia Bejan
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  2. Mircea Crasmareanu
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Correspondence to Mircea Crasmareanu.

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Dedicated to the memory of Professor Dr. Mircea Craioveanu.

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Bejan, C.L., Crasmareanu, M. Second order parallel tensors and Ricci solitons in \(3\)-dimensional normal paracontact geometry. Ann Glob Anal Geom 46, 117–127 (2014). https://doi.org/10.1007/s10455-014-9414-4

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  • DOI: https://doi.org/10.1007/s10455-014-9414-4

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