Para-Ricci-like Solitons with Arbitrary Potential on Para-Sasaki-like Riemannian π-Manifolds

Article Multidisciplinary Sciences

Para-Ricci-like Solitons with Vertical Potential on Para-Sasaki-like Riemannian π-Manifolds

Hristo Manev

Summary: The study focuses on para-Ricci-like solitons on certain types of Riemannian manifolds, considering different scenarios related to the soliton potential. By proving additional geometric properties and obtaining results related to parallel symmetric second-order covariant tensor on the manifolds, support is provided for the given assertions. An explicit example in dimension 5 is presented to illustrate the findings.

SYMMETRY-BASEL (2021)

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Article Mathematics

Para-Sasaki-like Riemannian manifolds and new Einstein metrics

Stefan Ivanov et al.

Summary: In this paper, a new class of para-Sasaki-like Riemannian manifolds are determined, and explicit examples are provided. A hyperbolic extension of a paraholomorphic paracomplex Riemannian manifold is defined and shown to be a para-Sasaki-like Riemannian manifold. Additionally, new examples of complete Einstein Riemannian manifolds of negative scalar curvature are presented.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS (2021)

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Article Mathematics

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

Hristo Manev et al.

Summary: A new type of soliton with a potential Reeb vector field on Riemannian manifolds with an almost paracontact structure has been introduced and studied. Special cases such as para-Einstein-like, para-Sasaki-like, and having a torse-forming Reeb vector field were considered. A necessary and sufficient condition for the manifold to admit a para-Ricci-like soliton, similar to para-Einstein, was proven, with explicit examples provided in support.

MATHEMATICS (2021)

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Article Mathematics, Applied