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arXiv · 2606.23184

Hyperbolic solitons on trans-Sasakian space forms and its submanifolds

Bidhan Mondal·Sibsankar Panda·Nirabhra Basu
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Abstract

Kong and Liu introduced the concept of hyperbolic Ricci flow in 2007 and used it to study the wave character of metrics. After that, many mathematicians have used this new geometric flow to study the evolution of manifolds and their structures. Ricci solitons and hyperbolic Ricci solitons are self-similar solitons of the Ricci flow and hyperbolic Ricci flow respectively. In this paper, we introduce the concept of hyperbolic $*-$Ricci solitons and hyperbolic Ricci-Yamabe solitons on a trans-Sasakian space forms and characterized the nature of some hyperbolic solitons. Additionally, we deduce the Ricci tensors of submanifolds of trans-Sasakian space forms and conformal trans-Sasakian space form and found the nature of solitons on submanifolds. Finally, we have included an example which will justify our result.

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Bidhan Mondal, Sibsankar Panda, Nirabhra Basu. 2026-06-22. Hyperbolic solitons on trans-Sasakian space forms and its submanifolds. https://arxiv.org/abs/2606.23184

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