Finite topological type of complete gradient shrinking GRF system solitons

Articles in Press

Document Type : Original Article

Authors

1 Department of mathematics, Faculty of mathematics and computers sciences, Shahid Chamran University of Ahvaz, Ahvaz, Iran

2 Department of Mathematics, Faculty of Mathematical and Computer Sciences, Shahid Chamran University of Ahvaz, Ahvaz, Iran

Abstract

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.

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References

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Journal of Finsler Geometry and its Applications

Articles in Press, Accepted Manuscript
Available Online from 17 November 2025

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