Para-Ricci-Like Solitons on Riemannian Manifolds with Almost Paracontact Structure and Almost Paracomplex Structure

Hristo Manev and Mancho Manev
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Hristo Manev: Department of Medical Informatics, Biostatistics and E-Learning, Faculty of Public Health, Medical University of Plovdiv, 15A Vasil Aprilov Blvd, 4002 Plovdiv, Bulgaria
Mancho Manev: Department of Medical Informatics, Biostatistics and E-Learning, Faculty of Public Health, Medical University of Plovdiv, 15A Vasil Aprilov Blvd, 4002 Plovdiv, Bulgaria

Mathematics, 2021, vol. 9, issue 14, 1-10

Abstract: We introduce and study a new type of soliton with a potential Reeb vector field on Riemannian manifolds with an almost paracontact structure corresponding to an almost paracomplex structure. The special cases of para-Einstein-like, para-Sasaki-like and having a torse-forming Reeb vector field were considered. It was proved a necessary and sufficient condition for the manifold to admit a para-Ricci-like soliton, which is the structure that is para-Einstein-like. Explicit examples are provided in support of the proven statements.

Keywords: para-Ricci-like soliton; ?-Ricci soliton; para-Einstein-like manifold; ?-Einstein manifold; almost paracontact structure; almost paracomplex structure; Riemannian manifold; torse-forming vector field (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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