Nature of Some Solitons on Almost coKähler Manifolds and Asymptotically Harmonic Manifolds

2023/05/11 by Ghosh, Paritosh, Shah, Hemangi Madhusudan, Bhattacharyya, Arindam
#53B20 #53B40 #53C25 #53D15 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.06597

Abstract

In this research, we study the nature of η-Einstein and gradient η-Einstein soliton in the framework of almost coKähler manifolds and (κ, μ)-almost coKähler manifolds. We find some expressions for scalar curvature of the almost coKähler manifold admitting η-Einstein soliton in various cases. We also prove that if a (κ, μ)-almost coKähler manifold admits a gradient η-Einstein soliton, then either the manifold is coKähler, or N(κ)-almost coKahler, or the soliton is trivial. We present an example which validates our results. Finally, we investigate the asymptotically harmonic manifolds admitting non-trivial Ricci solitons and show that they exhibit rigid behavior if for example, scalar curvature attains maximum.

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