Hessian流形上两个特殊泛函的Euler-Lagrange方程

The Euler-Lagrange Equations of Two Special Functionals on Hessian Geometry

本文主要研究Hessian几何上Koszul形式和泛函变分问题。首先给出Hessian几何中Hessian结构、Koszul形式、Hessian曲率概念及相关性质,然后在Hessian流形上计算了Hessian曲率Q、第二Koszul形式β及Tr(β)的变分,最后计算了两个特殊泛函的Euler-Lagrange方程。

This paper focuses on the Koszul forms and functional variation problems on Hessian geometry. Firstly, the concept and properties of Hessian structures, the Koszul forms and Hessian curvature are given. Then, we calculate the variation of Hessian curvature Q, the second Koszul form β, its trace Tr(β). Finally, we calculate the Euler-Lagrange equations of two special functionals on Hessian geometry.