Related papers: k-Harmonic immersion and submersion into a sphere

This note reviews some of the recent work on biharmonic conformal maps (see \cite{OC}, Chapter 11, for a detailed survey). It will be focused on biharmonic conformal immersions and biharmonic conformal maps between manifolds of the same…

We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various…

We present a construction method for triharmonic maps to spheres. In particular, we show that for any $m\in\mathbb{N}$ with $m\geq 3$ there exists a triharmonic map from $\mathbb{R}^m\setminus\{0\}$ into a round sphere. In addition, we…

We give a complete classification of local and global conformal biharmonic maps between any two space forms by proving that a conformal map between two space forms is proper biharmonic if and only if the dimension is 4, the domain is flat,…

We discuss a method to construct Dirac-harmonic maps developed by J.~Jost, X.~Mo and M.~Zhu in J.~Jost, X.~Mo, M.~Zhu, \emph{Some explicit constructions of Dirac-harmonic maps}, J. Geom. Phys. \textbf{59} (2009), no. 11, 1512--1527.The…

In this paper, we address several interconnected problems in the theory of harmonic maps between Riemannian manifolds. First, we present necessary background and establish one of the main results of the paper: a criterion characterizing…

We classify the biharmonic Legendre curves in a Sasakian space form, and obtain their explicit parametric equations in the $(2n+1)$-dimensional unit sphere endowed with the canonical and deformed Sasakian structures defined by Tanno. Then,…

Laplacian eigenmodes on homogeneous Clifford--Klein factors of the three--sphere are obtained as pullbacks of harmonics on the orbifolded two--sphere using the Hopf map. A method of obtaining these polyhedral, or crystal, harmonics using…

We characterise the maps into the space of $2$-spheres in $S^n$ that are the conformal Gauss maps of conformal immersions of a surface. In particular, we give an invariant formulation and efficient proof of a characterisation, due to…

For biharmonic maps, there is a famous conjecture named Chen's conjecture. In later paper, Wang and Ou gave an affirmative partial answer to submersion version of Chen's conjecture. In this paper, we give an affirmative partial answer to…

We give three formulas expressing the Smale invariant of an immersion f of a (4k-1)-sphere into (4k+1)-space. The terms of the formulas are geometric characteristics of any generic smooth map g of any oriented 4k-dimensional manifold, where…

We give the twistor description of harmonic maps of the Riemann sphere into the Hilbert-Schmidt Grassmannian. The study of such maps is motivated by the harmonic spheres conjecture formulated in the beginning of this paper.

We continue our study [Ou4] of f-biharmonic maps and f-biharmonic submanifolds by exploring the applications of f-biharmonic maps and the relationships among biharmonicity, f-biharmonicity and conformality of maps between Riemannian…

Inspired by the all-important conformal invariance of harmonic maps on two-dimensional domains, this article studies the relationship between biharmonicity and conformality. We first give a characterization of biharmonic morphisms,…

We give several construction methods and use them to produce many examples of proper biharmonic maps including biharmonic tori of any dimension in Euclidean spheres (Theorem 2.2, Corollaries 2.3, 2.4, and 2.6), biharmonic maps between…

In this note, we generalize biharmonic equation for rotationally symmetric maps ([4], [16], [10]) to equivariant maps between model spaces and use it to give a complete classification of rotationally symmetric conformal biharmonic maps from…

In this note, we show that some F-harmonic maps into spheres are global maxima of the variations of their energy functional on the conformal group of the sphere. Our result extends partially those obtained in [15] and [17] for harmonic and…

In this paper, we discuss the associated family of harmonic maps $\mathcal{F}: M \rightarrow G/K$ from a Riemann surface $M$ into inner symmetric spaces of compact or non-compact type which are either algebraic or totally symmetric. These…

In the present paper, we study bi-$f$-harmonic maps which generalize not only $f$-harmonic maps, but also biharmonic maps. We derive bi-$f$-harmonic equations for curves in the Euclidean space, unit sphere, hyperbolic space, and in…

We call indexed-biharmonic maps, the solutions of a particular non linear elliptic PDE of order 4. This is a generalization of harmonic maps which verifies that biharmonic maps are biharmonic of index 0. The goal of this article is to study…