Geometry of Paracontact Manifolds Admitting Conformal Ricci-Yamabe Solitons

Abstract

This study investigates the classification of conformal Ricci-Yamabe solitons within the framework of paracontact geometry. In particular, we analyze the structural properties of para-Kenmotsu manifolds that satisfy the conditions for conformal Ricci-Yamabe solitons, with special attention to three-dimensional cases exhibiting conformal gradient Ricci-Yamabe solitons. In addition, we provide a comprehensive classification of para-Sasakian and para-cosymplectic manifolds that admit conformal Ricci-Yamabe solitons and its gradient form conformal gradient Ricci-Yamabe solitons. To substantiate the theoretical findings, an explicit example is constructed and discussed in detail.

Keywords: Paracontact manifolds; self-similar solution; conformal Ricci-Yamabe solitons; Einstein manifolds.

2010 Mathematics Subject Classification. 53B30; 53C21; 53C25