共查询到20条相似文献,搜索用时 31 毫秒
1.
Bayram Sahin 《Proceedings Mathematical Sciences》2008,118(4):573-581
We study harmonic Riemannian maps on locally conformal Kaehler manifolds (lcK manifolds). We show that if a Riemannian holomorphic
map between lcK manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map
under a condition. When the domain is Kaehler, we prove that a Riemannian holomorphic map is harmonic if and only if the lcK
manifold is Kaehler. Then we find similar results for Riemannian maps between lcK manifolds and Sasakian manifolds. Finally,
we check the constancy of some maps between almost complex (or almost contact) manifolds and almost product manifolds. 相似文献
2.
The paper shows that any Jacobi field along a harmonic map fromthe 2-sphere to the complex projective plane is integrable (thatis, is tangent to a smooth variation through harmonic maps).This provides one of the few known answers to the problem ofintegrability, which was raised in different contexts of geometryand analysis. It implies that the Jacobi fields form the tangentbundle to each component of the manifold of harmonic maps fromS2 to CP2 thus giving the nullity of any such harmonic map;it also has a bearing on the behaviour of weakly harmonic E-minimizingmaps from a 3-manifold to CP2 near a singularity and the structureof the singular set of such maps from any manifold to CP2. 相似文献
3.
The Teichmüller harmonic map flow, introduced by Rupflin and Topping (2012) [11], evolves both a map from a closed Riemann surface to an arbitrary compact Riemannian manifold, and a constant curvature metric on the domain, in order to reduce its harmonic map energy as quickly as possible. In this paper, we develop the geometric analysis of holomorphic quadratic differentials in order to explain what happens in the case that the domain metric of the flow degenerates at infinite time. We obtain a branched minimal immersion from the degenerate domain. 相似文献
4.
We investigate a parabolic-elliptic system which is related to a harmonic map from a compact Riemann surface with a smooth boundary into a Lorentzian manifold with a warped product metric.We prove that there exists a unique global weak solution for this system which is regular except for at most finitely many singular points. 相似文献
5.
Volker Branding 《Archiv der Mathematik》2018,111(3):329-336
We prove a Liouville-type theorem for biharmonic maps from a complete Riemannian manifold of dimension \(n\) that has a lower bound on its Ricci curvature and positive injectivity radius into a Riemannian manifold whose sectional curvature is bounded from above. Under these geometric assumptions we show that if the \(L^p\)-norm of the tension field is bounded and the n-energy of the map is sufficiently small, then every biharmonic map must be harmonic, where \(2<p<n\). 相似文献
6.
Harmonic morphisms as unit normal bundles¶of minimal surfaces 总被引:2,自引:0,他引:2
Let be an isometric immersion between Riemannian manifolds and be the unit normal bundle of f. We discuss two natural Riemannian metrics on the total space and necessary and sufficient conditions on f for the projection map to be a harmonic morphism. We show that the projection map of the unit normal bundle of a minimal surface in a Riemannian
manifold is a harmonic morphism with totally geodesic fibres.
Received: 6 February 1999 相似文献
7.
In this paper,we show that every harmonic map from a compact K?hler manifold with uniformly RC-positive curvature to a Riemannian manifold with non-positive complex sectional curvature is constant.In particular,there is no non-constant harmonic map from a compact Koahler manifold with positive holomorphic sectional curvature to a Riemannian manifold with non-positive complex sectional curvature. 相似文献
8.
Yuanlong Xin 《数学学报(英文版)》1999,15(2):277-292
Some Liouville type theorems for harmonic maps from Kähler manifolds are obtained. The main result is to prove that a harmonic map from a bounded symmetric domain (exceptR IV(2)) to any Riemannian manifold with finite energy has to be constant. 相似文献
9.
Tom Y. H. Wan 《Proceedings of the American Mathematical Society》2001,129(2):567-572
We show that a decomposition theorem of Duren-Hengartner about planar harmonic maps can be generalized to give a necessary and sufficient condition for a harmonic map between smooth surfaces to be decomposable as a holomorphic map followed by a univalent harmonic embedding.
10.
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
11.
Roger Moser 《Mathematische Zeitschrift》2003,243(2):263-289
Let be open and a smooth, compact Riemannian manifold without boundary. We consider the approximated harmonic map equation for maps , where . For , we prove H?lder continuity for weak solution s which satisfy a certain smallness condition. For , we derive an energy estimate which allows to prove partial regularity for stationary solutions of the heat flow for harmonic
maps in dimension .
Received: 7 May 2001; / in final form: 22 February 2002 Published online: 2 December 2002 相似文献
12.
We prove that given a simply connected compact manifold M and a
closed manifold N, any map in the Sobolev space W
1,2(M,N) can be
approximated weakly by smooth maps between M and N.
Submitted: September 2002, Final version: November 2002. 相似文献
13.
Paul Baird 《Annals of Global Analysis and Geometry》1992,10(1):63-72
Let be a harmonic mapping from a Riemannian 3-manifold to a Riemannian 2-manifold. A smooth function on M is associated to , derived from the eigenvalues of the first fundamental form, the vanishing of which is equivalent to being a harmonic morphism. The Laplacian of this function is computed and a maximum principle applied to derive criteria when a harmonic map must be a harmonic morphism. 相似文献
14.
Jiaping Wang 《Journal of Geometric Analysis》1998,8(3):485-514
We consider the existence, uniqueness and convergence for the long time solution to the harmonic map heat equation between
two complete noncompact Riemannian manifolds, where the target manifold is assumed to have nonpositive curvature. As an application,
we solve the Dirichlet problem at infinity for proper harmonic maps between two hyperbolic manifolds for a class of boundary
maps. The boundary map under consideration has finite many points at which either it is not differentiable or has vanishing
energy density. 相似文献
15.
Roger Moser 《manuscripta mathematica》2001,105(3):379-399
We prove existence and uniqueness of weakly harmonic maps from the unit ball in ℝ
n
(with n≥ 3) to a smooth compact target manifold within the class of maps with small scaled energy for suitable boundary data.
Received: 9 June 2000 / Revised version: 17 April 2001 相似文献
16.
Hu Hesheng 《数学年刊B辑(英文版)》1984,5(4):737-740
It is proved that a harmonic map or a relative harmonic map from Euclidean space $\[{R^n}(n \ne 2)\]$ into an m-dimensional Riemannian manifold $\[{M_m}\]$ with finite energy or slowly divergent energy must be a constant map. Some physical applications are also presented. 相似文献
17.
In this article, we define a new class of middle dimensional submanifolds of a Hyperkähler manifold which contains the class of complex Lagrangian submanifolds, and show that this larger class is invariant under the mean curvature flow. Along the flow, the complex phase map satisfies the generalized harmonic map heat equation. It is also related to the mean curvature vector via a first order differential equation. Moreover, we proved a result on nonexistence of Type I singularity. 相似文献
18.
Yong Hah Lee 《Potential Analysis》2014,41(2):463-468
We prove that given any continuous data f on the harmonic boundary of a complete Riemannian manifold with image within a ball in the normal range, there exists a harmonic map from the manifold into the ball taking the same boundary value at each harmonic boundary point as that of f. 相似文献
19.
Ma Li 《Commentarii Mathematici Helvetici》1991,66(1):279-301
In this paper, we study the harmonic map heat flow with free boundary from a Riemannian surface with smooth boundary into
a compact Riemannian manifold. As a consequence, we get at least one disk-type minimal surface in a compact Riemannian manifold
without minimal 2-sphere. 相似文献
20.
Shuichi Jimbo 《Journal of Differential Equations》2003,188(2):447-460
We prove that any non-constant smooth static solution to a geometric parabolic system is unstable, provided that the domain is convex. As the important applications, we shall consider the Landau-Lifshitz equation and the heat flow for harmonic map. 相似文献