Finite topological type of complete gradient shrinking GRF system solitons

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.

کلیدواژه ها:

General Ricci flow ، soliton ، shrinking ، finite topological type