University of Mohaghegh Ardabili Journal of Finsler Geometry and its Applications 2783-0500 7 1 2026 05 01 Finite topological type of complete gradient shrinking GRF system solitons 123 129 4238 10.22098/jfga.2025.18311.1182 EN Mohamad Yar Ahmadi Department of mathematics, Faculty of mathematics and computers sciences, Shahid Chamran University of Ahvaz, Ahvaz, Iran Sina Hedayatian Department of Mathematics, Faculty of Mathematical and Computer Sciences, Shahid Chamran University of Ahvaz, Ahvaz, Iran Journal Article 2025 09 09 This paper investigates the properties and topological implications of gradient shrinking general Ricci flow (GRF) system solitons. A GRF system soliton is a solution that evolves through a one-parameter family of diffeomorphisms or scaling transformations. Under specific geometric constraints, such as bounded Ricci curvature or positive injectivity radius, we establish a lower bound for the potential function associated with these solitons. Furthermore, we demonstrate that any complete gradient shrinking GRF system soliton exhibits finite topological type. These results extend the understanding of geometric flows, linking them to broader applications in differential geometry and topology. https://jfga.uma.ac.ir/article_4238_b775852b4e50e64ace9b89f30e5c7354.pdf