What question did this study set out to answer?

To explore structural equations for compact hyperbolic Ricci solitons with 2-conformal vector fields and derive implications.

April 3, 2026Open Access

Some characterizations for compact hyperbolic Ricci solitons admitting 2-conformal vector fields

FSFarzaneh ShahmkhaliImam Khomeini International University GFGhodratallah Fasihi-RamandiImam Khomeini International University UDUday DeUniversity of Calcutta

Key Points

To explore structural equations for compact hyperbolic Ricci solitons with 2-conformal vector fields and derive implications.
Derived structural equations for hyperbolic Ricci solitons
Obtained an integral formula for compact manifolds
Applied the Hodge-de Rham decomposition theorem
Identified that a non-trivial compact hyperbolic Ricci soliton with 2-conformal fields is isometric to a Euclidean sphere
Established that such manifolds either have constant scalar curvature or conformal vector fields

Abstract

In this paper, we find a set of structural equations for hyperbolic Ricci solitons admitting 2-conformal vector fields, which extends similar results for Ricci solitons. As a result of these equations, we obtain an integral formula for the case when the underlying manifold is compact, indicating that a non-trivial compact hyperbolic Ricci soliton with 2-conformal potential vector field is isometric to Euclidean sphere. Also, it will be shown that such manifolds either have constant scalar curvature or their associated vector fields are conformal. Furthermore, we use the Hodge-de Rham decomposition theorem to establish a link with 2-conformal vector fields associated with a hyperbolic Ricci soliton.

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