Kähler-Finsler流形到Riemann流形的调和映照  

Harmonic maps from Kähler-Finsler manifolds to Riemannian manifolds

作　　者：李鸿军 邱春晖[2] Hongjun Li;Chunhui Qiu

机构地区：[1]河南大学数学与统计学院,开封475004 [2]厦门大学数学科学学院,厦门361005

出　　处：《中国科学：数学》2024年第10期1585-1602,共18页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:12001165和11971401)资助项目。

摘　　要：本文首先给出Kähler-Finsler流形到Riemann流形光滑映照的■-能量泛函的第一变分公式,利用Jost和Yau关于Hermite调和映照的存在定理,得到Kähler-Finsler流形到Riemann流形调和映照的存在定理.其次,给出Kähler-Finsler流形到Riemann流形调和映照的第二变分公式,作为应用,证明目标Riemann流形具有非正复截面曲率时,调和映照是稳定的.最后,讨论Kähler-Finsler流形到Kähler流形调和映照的第二变分公式,目标Kähler流形的曲率张量是强非正时,调和映照是稳定的.In this paper,we first derive the first variation formula of the■-energy functional for a smooth map from a Kähler-Finsler manifold to a Riemannian manifold.By applying the existence theorem proved by Jost and Yau for Hermitian harmonic maps,we obtain an existence theorem for harmonic maps from Kähler-Finsler manifolds to Riemannian manifolds.Next,we derive the second variation formula of harmonic maps from a Kähler-Finsler manifold to a Riemannian manifold.As an application,we prove that harmonic maps are stable if the target Riemannian manifold has non-positive complex sectional curvature.At last,we discuss the second variation formulas of harmonic maps from a Kähler-Finsler manifold to a Kähler manifold and prove that harmonic maps are stable if curvature tensors of the target Kähler manifold are strongly non-positive.

关 键 词：调和映照 ■-能量泛函 第二变分 Kähler-Finsler流形 

分 类 号：O186.1[理学—数学]