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We obtain conditions on the Lee form under which a holomorphic map between almost Hermitian manifolds is a harmonic map or morphism. Then we discuss under what conditions (i) the image of a holomorphic map from a cosymplectic manifold is…

dg-ga · Mathematics 2008-02-03 S. Gudmundsson , J. C. Wood

Both bi-harmonic map and $f$-harmonic map have nice physical motivation and applications. In this paper, by combination of these two harmonic maps, we introduce and study $f$-bi-harmonic maps as the critical points of the $f$-bi-energy…

Differential Geometry · Mathematics 2015-03-20 Wei-Jun Lu

In this paper, we investigate the relationships between linear measure and harmonic mappings.

Complex Variables · Mathematics 2016-12-06 Shaolin Chen , Gang Liu , Saminathan Ponnusamy

On non-K\"ahler manifolds the notion of harmonic maps is modified to that of Hermitian harmonic maps in order to be compatible with the complex structure. The resulting semilinear elliptic system is {\it not} in divergence form. The case of…

Differential Geometry · Mathematics 2009-02-27 Hans-Christoph Grunau , Marco Kuehnel

We describe work on solutions of certain non-divergence type and therefore non-variational elliptic and parabolic systems on manifolds. These systems include Hermitian and affine harmonics which should become useful tools for studying…

Differential Geometry · Mathematics 2010-11-16 Jürgen Jost , Fatma Muazzez Şimşir

By studying cohomology classes that are related with $p$-harmonic morphisms, $F$-harmonic maps, and $f$-harmonic maps, we extend several of our previous results on Riemannian submersions and $p$-harmonic morphisms to $F$-harmonic maps, and…

Differential Geometry · Mathematics 2023-03-22 Bang-Yen Chen , Shihshu Walter Wei

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…

Differential Geometry · Mathematics 2010-12-17 Jürgen Jost , Fatma Muazzez Şimşir

In this paper, we show that one can interrelate pluriharmonic maps with para-pluriharmonic maps by means of the loop group method. As an appendix, we give examples for the interrelation between pluriharmonic maps and para-pluriharmonic…

Differential Geometry · Mathematics 2010-12-03 Nobutaka Boumuki , Josef Dorfmeister

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…

Differential Geometry · Mathematics 2025-07-14 Sergey Stepanov , Irina Tsyganok

In this paper, we prove that the class of bi-f-harmonic maps and that of f-biharmonic maps from a conformal manifold of dimension not equal to 2 are the same (Theorem 1.1). We also give several results on nonexistence of proper…

Differential Geometry · Mathematics 2018-08-08 Yong Luo , Ye-Lin Ou

In this paper, we present several necessary and sufficient conditions for a logharmonic mapping to be normal i.e., we establish Marty's criterion, Zalcman-Pang lemma and the Lohwater-Pommerenke theorem for logharmonic mappings, along with…

Complex Variables · Mathematics 2025-05-26 Molla Basir Ahamed , Sanju Mandal

We give coefficient estimates for a class of close-to-convex harmonic mappings, and discuss the Fekete-Szeg\H{o} problem of it. We also introduce two classes of polyharmonic mappings $\mathcal{HS}_{p}$ and $\mathcal{HC}_{p}$, consider the…

Complex Variables · Mathematics 2013-10-01 Jiaolong Chen , Antti Rasila , Xiantao Wang

The first result in this study is a non-existence theorem for $\alpha-$harmonic mappings. Additionally, a direct connection between the $\alpha-$ harmonic and harmonic maps is made possible via conformal deformation. Second, the instability…

Differential Geometry · Mathematics 2022-08-26 Seyed Mehdi Kazemi Torbaghan , Keyvan Salehi

f-Harmonic maps were first introduced and studied by Lichnerowicz in \cite{Li} (see also Section 10.20 in Eells-Lemaire's report \cite{EL}). In this paper, we study a subclass of f-harmonic maps called f-harmonic morphisms which pull back…

Differential Geometry · Mathematics 2011-03-30 Ye-Lin Ou

On foliations, there are two kinds of harmonic maps, that is, transversally harmonic map and $(F,F')$-harmonic map which are equivalent when the foliation is minimal. In this paper, we study transversally f-harmonic and $(F,F')_f$-harmonic…

Differential Geometry · Mathematics 2023-08-15 Xueshan Fu , Jinhua Qian , Seoung Dal Jung

In this work we construct a variety of new complex-valued proper biharmonic maps and (2,1)-harmonic morphisms on Riemannian manifolds with non-trivial geometry. These are solutions to a non-linear system of partial differential equations…

Differential Geometry · Mathematics 2023-03-14 Elsa Ghandour , Sigmundur Gudmundsson

This article has two purposes. The first is to give an expository account of the integrable systems approach to harmonic maps from surfaces to Lie groups and symmetric spaces, focusing on spectral curves for harmonic 2-tori. The most…

Differential Geometry · Mathematics 2012-11-14 Emma Carberry

In this paper, we extend the definition of p-harmonic and p-biharmonic maps between Riemannian manifolds. We present some new properties for the generalized stable p-harmonic maps.

Differential Geometry · Mathematics 2022-03-10 Bouchra Merdji , Ahmed Mohammed Cherif

In this note, we extend the definition of $p$-biharmonic and bi-$p$-harmonic maps between two Riemannian manifolds and explore some of their properties.

Differential Geometry · Mathematics 2026-03-09 Fethi Latti , Ahmed Mohammed Cherif

In this paper, we define both the upper and lower order of a sense-preserving harmonic mapping in $\mathbb{D}$. We generalize to the harmonic case some known results about holomorphic functions with positive lower order and we show some…

Complex Variables · Mathematics 2021-07-06 Arbeláez , H. , Hernández , R. , Sierra W