second variation formula meaning in Chinese

第二变分公式

The second part consist of chapter four . in chapter one , we study the energy density of harmonic map from finsler manifold and generalize classical result in [ se ] . in chapter two , we obtain lower estimates for the first eigenvalue of the laplace operator on a compact finsler manifold , and it generalize lichnerowicz - obata theorem [ li ] [ ob ] . in chapter three , we derive the first and second variation formula for harmonic maps between finsler manifolds . as an application , some nonexistence theorems of nonconstant stable harmonic maps from a finsler manifold to a riemannian manifold are given
第一章讨论finsler流形到黎曼流形调和映射的能量密度的间隙性，推广了[ se ]中的结果。第二章对紧致finsler流形上laplace算子的第一特征值的下界作了估计，推广了黎曼流形上的lichnerowicz - obata定理[ li ] [ ob ] 。
One of open problems is to study harmonic maps between finsler manifolds and derive the first and second variation formula for harmonic maps between finsler manifolds . firstly , we define harmonic map between finsler manifold . in fact , it is the harmonic map from projective sphere bundle of source manifold to the projective sphere bundle of target manifold
算子的第一非零特征值凡全mk .特别地，当‘ ，二二k时， m的直径为六?当m是黎曼流形时，由moer “定理的推论直接可知m与半径为去的球等距