ON WARPED PRODUCT MANIFOLDS ADMITTING τ-QUASI RICCI-HARMONIC METRICS

Seçkin Günsen, Leyla Onat

DOI Number
https://doi.org/10.22190/FUMI211212023G
First page
333
Last page
343

Abstract


In this paper, we study warped product manifolds admitting $\tau$-quasi Ricci-harmonic(RH) metrics. We prove that the metric of the fibre is harmonic Einstein when warped product metric is $\tau$-quasi RH metric. We also provide some conditions for $M$ to be a harmonic Einstein manifold. Finally, we provide necessary and sufficient conditions for a metric $g$ to be $\tau$-quasi RH metric by using a differential equation system.

Keywords

warped products, gradient Ricci-Harmonic soliton, τ-quasi Ricci- Harmonic metric, Harmonic Einstein

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DOI: https://doi.org/10.22190/FUMI211212023G

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