Symmetries and Conservation Laws for the 2D Ricci Flow Model
Rodica Cimpoiasu
TL;DR
This paper explores the relationship between symmetries and conservation laws in the 2D Ricci flow model, deriving new similarity solutions and advancing understanding of its mathematical structure.
Contribution
It introduces a method to connect symmetries and conservation laws for the 2D Ricci flow, revealing new similarity solutions not previously documented.
Findings
Derived conservation laws from multipliers
Identified symmetries related to conservation laws
Discovered new similarity solutions
Abstract
The paper aims to study the connection between symmetries and conservation laws for the 2D Ricci flow model. The procedure starts by obtaining a set of multipliers which generates conservation laws. Then, using a general relation which connects symmetries and conservation laws for whatever dynamical system, one determines symmetries related to a chosen multiplier. On this basis, new similarity solutions of the model, not yet discussed in literature, are highlighted.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds