On the equations defining the Ricci-flows of manifolds
Valerii Dryuma
TL;DR
This paper constructs examples of Ricci flows on four-dimensional manifolds using nonlinear differential equations similar to Monge-Ampere, analyzing their solutions and properties.
Contribution
It introduces a method to generate Ricci flow examples on 4D manifolds via Monge-Ampere type equations, expanding understanding of Ricci flow solutions.
Findings
Constructed explicit Ricci flow examples on four-dimensional manifolds.
Analyzed particular solutions and their properties.
Demonstrated the role of nonlinear differential equations in Ricci flow analysis.
Abstract
The examples of the Ricci flows on four-dimendionsl manifolds which are determined by help of nonlinear differentials equations of the type of Monge-Ampere are constructed. Their particular solutions and their properties are discussed.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Black Holes and Theoretical Physics