Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Para-Ricci-like Solitons on Almost Paracontact Almost Paracomplex Riemannian Manifolds

Version 1 : Received: 25 June 2021 / Approved: 25 June 2021 / Online: 25 June 2021 (12:31:06 CEST)

How to cite: Manev, H.; Manev, M. Para-Ricci-like Solitons on Almost Paracontact Almost Paracomplex Riemannian Manifolds. Preprints 2021, 2021060622 (doi: 10.20944/preprints202106.0622.v1). Manev, H.; Manev, M. Para-Ricci-like Solitons on Almost Paracontact Almost Paracomplex Riemannian Manifolds. Preprints 2021, 2021060622 (doi: 10.20944/preprints202106.0622.v1).

## Abstract

It is introduced and studied para-Ricci-like solitons with potential Reeb vector field on almost paracontact almost paracomplex Riemannian manifolds. The special cases of para-Einstein-like, para-Sasaki-like and having a torse-forming Reeb vector field have been considered. It is proved a necessary and sufficient condition the manifold to admit a para-Ricci-like soliton which is the structure to be para-Einstein-like. Explicit examples are provided in support of the proven statements.

## Keywords

para-Ricci-like soliton; $\eta$-Ricci soliton; para-Einstein-like manifold; $\eta$-Einstein manifold; almost paracontact almost paracomplex Riemannian manifold; torse-forming vector field

## Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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