Harmonic maps from Finsler manifolds
Harmonic maps from Finsler manifolds
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DOI：
10.1215/ijm/1258138069
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发表时间：
2001-10
影响因子：
0.6
通讯作者：
X. Mo
中科院分区：
文献类型：
--
作者：
X. Mo
. Finsler流形是没有二次约束的黎曼流形。本文引入了从Finsler流形到Riemann流形的光滑映射φ的能量泛函、Euler-Lagrange算子和应力-能量张量。我们证明了φ是能量泛函的极值当且仅当φ萨蒂斯相应的Euler-Lagrange方程。我们还刻画了弱兰茨贝格流形的调和性和水平守恒性。利用张力场的测地系数表示，我们构造了既不是黎曼流形也不是闵可夫斯基流形的Berwald流形上调和映射的新例子.
. A Finsler manifold is a Riemannian manifold without the quadratic restriction. In this paper we introduce the energy functional, the Euler-Lagrange operator, and the stress-energy tensor for a smooth map φ from a Finsler manifold to a Riemannian manifold. We show that φ is an extremal of the energy functional if and only if φ satisfies the corresponding Euler-Lagrange equation. We also characterize weak Landsberg manifolds in terms of harmonicity and horizontal conservativity. Using the representation of a tension field in terms of geodesic coefficients, we construct new examples of harmonic maps from Berwald manifolds which are neither Riemannian nor Minkowskian.