Results 21 to 30 of about 2,667,437 (304)
Analysis, 2009 We introduce a class of maps from an affine flat into a Riemannian manifold that solve an elliptic system defined by the natural second order elliptic operator of the affine structure and the nonlinear Riemann geometry of the target. These maps are called affine harmonic.
Şimşir, Fatma Muazzez, Jost J.
openaire +4 more sources
Proceedings of the American Mathematical Society, 1958 1. Suppose that the functions x=x(a, 3), y=y(a, f) define a oneto-one harmonic mapping of the unit disc P in the a, p3-plane (a+i3 ==y) onto a convex domain C in the x, y-plane (x+iy=z). The origin is assumed to be fixed. Introducing two functions F(y) and G(y) which, in r, depend analytically upon the variable y we may write z = Re F(,y) +i Re G(y ...
openaire +2 more sources
On the bi-harmonic maps with potential
Arab Journal of Mathematical Sciences, 2018 In this note we characterize the harmonic maps and biharmonic maps with potential, and we prove that every biharmonic map with potential on a complete manifold satisfying some conditions is a harmonic map with potential.
Ahmed Mohammed Cherif, Mustapha Djaa
doaj +1 more source
Harmonic Maps on Kenmotsu Manifolds
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2013 We study in this paper harmonic maps and harmonic morphisms on Kenmotsu manifolds. We also give some results on the spectral theory of a harmonic map for which the target manifold is a Kenmotsu manifold.
Rehman Najma Abdul
doaj +1 more source
A harmonic maps approach to fluid flows [PDF]
, 2016 We obtain a complete solution to the problem of classifying all two-dimensional ideal fluid flows with harmonic Lagrangian labelling maps; thus, we explicitly provide all solutions, with the specified structural property, to the incompressible two ...
O. Constantin, María J. Martín
semanticscholar +1 more source
Convergence of Harmonic Maps [PDF]
The Journal of Geometric Analysis, 2015 In this paper we prove a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds.
openaire +2 more sources
Arab Journal of Mathematical Sciences, 2016 In this paper, we prove that a map between Riemannian manifolds is an f-harmonic morphism in a general sense if and only if it is horizontally weakly conformal, satisfying some conditions, and we investigate the properties of f-harmonic morphism in a ...
Nour Elhouda Djaa, Ahmed Mohamed Cherif
doaj +1 more source
A regularity theory for intrinsic minimising fractional harmonic maps
Calculus of Variations and Partial Differential Equations, 2018 We define and develop an interior partial regularity theory for intrinsic energy minimising fractional harmonic maps from Euclidean space into smooth compact Riemannian manifolds for fractional powers strictly between zero and one.
James Roberts
semanticscholar +1 more source
Harmonic Mappings of Spheres [PDF]
American Journal of Mathematics, 1972 This thesis is addressed to the following fundamental problem: given a homotopy class of maps between compact Riemannian manifolds N and M, is there a harmonic representative of that class? Eells and Sampson have given a general existence theorem for the case that M has no positive sectional curvatures [ESJ.\ud Otherwise, very little is known ...
openaire +6 more sources
Biharmonic maps on V-manifolds
International Journal of Mathematics and Mathematical Sciences, 2001 We generalize biharmonic maps between Riemannian manifolds into the case of the domain being V-manifolds. We obtain the first and second variations of biharmonic maps on V-manifolds.
Yuan-Jen Chiang, Hongan Sun
doaj +1 more source