TL;DR
This paper investigates the hyperbolic Kahler-Ricci flow, deriving its equations and evolution of geometric quantities, and simplifies it to a scalar hyperbolic Monge-Ampere equation on Calabi-Yau manifolds.
Contribution
It introduces a hyperbolic version of the Kahler-Ricci flow, deriving key equations and simplifying them on Calabi-Yau manifolds, expanding the understanding of geometric flows.
Findings
Derived the hyperbolic Kahler-Ricci flow equations
Calculated evolution of curvature and related quantities
Reduced the flow to a scalar hyperbolic Monge-Ampere equation on Calabi-Yau manifolds
Abstract
In this paper, the author has considered the hyperbolic Kahler-Ricci flow introduced by Kong and Liu [11], that is, the hyperbolic version of the famous Kahler-Ricci flow. The author has explained the derivation of the equation and calculated the evolutions of various quantities associated to the equation including the curvatures. Particularly on Calabi-Yau manifolds, the equation can be simplified to a scalar hyperbolic Monge-Ampere equation which is just the hyperbolic version of the corresponding one in Kahler-Ricci flow.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Differential Geometry Research