共查询到10条相似文献,搜索用时 46 毫秒
1.
In this paper,we consider the existence of harmonic maps from a Finsler manifold and study the characterisation of harmonic maps,in the spirit of Ishihara.Using heat quation method we show that any map from a compact Finsler manifold M to a compact Riemannian manifold with non-positive sectional curvature can be deformed into a harmonic map which has minimum energy in its homotopy class. 相似文献
2.
MO Xiaohuan~ YANG Yunyan~.LMAM School of Mathematical Sciences Peking University Beijing China.Department of Mathematics Renmin University of China Beijing China 《中国科学A辑(英文版)》2005,48(1):115-130
In this paper,we consider the existence of harmonic maps from a Finsler man-ifold and study the characterisation of harmonic maps,in the spirit of lshihara.Using heatequation method we show that any map from a compact Finsler manifold M to a com-pact Riemannian manifold with non-positive sectional curvature can be deformed into aharmonic map which has minimum energy in its homotopy class. 相似文献
3.
Wei Zhu 《高校应用数学学报(英文版)》2010,25(2):236-242
This paper studies the stability of P-harmonic maps and exponentially harmonic maps from Finsler manifolds to Riemannian manifolds by an extrinsic average variational method in the calculus of variations. It generalizes Li's results in [2] and [3]. 相似文献
4.
Atsushi Tachikawa 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009,26(5):1953-1970
We study the energy functional for maps from a Riemannian m-manifold M into a Finsler space N=(Rn,F). Under the restriction 2?m?4, we prove the full Hölder regularity of weakly harmonic maps (i.e., weak solutions of its Euler–Lagrange equation) from M to N in the case that the Finsler structure F(u,X) depends only on vectors X, and a partial Hölder regularity of energy minimizing maps in general cases. 相似文献
5.
The global existence of the heat flow for harmonic maps from noncompact manifolds is considered. When L^m norm of the gradient of initial data is small, the existence of a global solution is proved. 相似文献
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7.
Huang-jia Tian 《高校应用数学学报(英文版)》2014,29(2):217-229
In this paper, we give the equation that characterizes projective vector fields on a Finsler manifold by the local coordinate. Moreover, we obtain a feature of the projective fields on the compact Finsler manifold with non-positive flag curvature and the non-existence of projective vector fields on the compact Finsler manifold with negative flag curvature. Furthermore, we deduce some expectable, but non-trivial relationships between geometric vector fields such as projective, affine, conformal, homothetic and Killing vector fields on a Finsler manifold. 相似文献
8.
A horizontal (-δ)-Laplacian is defined on strongly pseudoconvex complex Finsler manifolds, first for functions and then for horizontal differential forms of type (p,q). The principal part of the (-δ)-Laplacian is computed in local coordinates. As an application, the (-δ)-Laplacian on strongly Kahler Finsler manifold is obtained explicitly in terms of the horizontal covariant derivatives of the Chern-Finsler conncetion. 相似文献
9.
朱微 《高校应用数学学报(A辑)》2011,26(3):335-342
把无焦点黎曼流形的概念推广到了Finsler流形中.通过在无焦点Finsler流形上构造凸函数,得到了Finsler流形间调和映射的一个刚性定理. 相似文献
10.
Let M be a smooth manifold with Finsler metric F,and let T M be the slit tangent bundle of M with a generalized Riemannian metric G,which is induced by F.In this paper,we prove that (i) (M,F) is a Landsberg manifold if and only if the vertical foliation F V is totally geodesic in (T M,G);(ii) letting a:= a(τ) be a positive function of τ=F 2 and k,c be two positive numbers such that c=2 k(1+a),then (M,F) is of constant curvature k if and only if the restriction of G on the c-indicatrix bundle IM (c) is bundle-like for the horizontal Liouville foliation on IM (c),if and only if the horizontal Liouville vector field is a Killing vector field on (IM (c),G),if and only if the curvature-angular form Λ of (M,F) satisfies Λ=1-a 2/R on IM (c). 相似文献