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Some Solitons on Homogeneous Almost $\alpha$-Cosymplectic $3$-Manifolds and Harmonic Manifolds

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arxiv 2301.02430 v2 pith:OJVHM3XB submitted 2023-01-06 math.GM

Naeem Ahmad Pundeer , Paritosh Ghosh , Hemangi Madhusudan Shah , Arindam Bhattacharyya This is my paper · ORCID
classification math.GM
keywords almostalphacosymplecticmanifoldseinsteinharmonichomogeneousmanifold
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abstract

In this paper, we investigate the nature of Einstein solitons, whether it is steady, shrinking or expanding on almost $\alpha$-cosymplectic $3$-manifolds. We also prove that a simply connected homogeneous almost $\alpha$-cosymplectic $3$-manifold, admitting a contact Einstein soliton, is an unimodular semidirect product Lie group. Finally, we show that a harmonic manifold admits a Ricci soliton if and only if it is flat.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Some Characteristics of Almost $\omega$-Bach Solitons

    math.DG 2025-05 reject novelty 5.0 of 10

    A new generalized Bach soliton is defined, but the explicit examples on S2 x H2, R2 x H2, and R2 x S2 do not satisfy the governing equations.

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