Journal ArticleDOI
Triharmonic morphisms between Riemannian manifolds
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In this article, the notion of k-polyharmonic morphisms is introduced, which preserves polyharmonic functions of order k. The morphisms are defined as maps between Riemannian manifolds that preserve harmonic functions and biharmonic function respectively.Abstract:
Polyharmonic functions have been studied in various fields. There are maps between Riemannian manifolds called harmonic morphisms and biharmonic morphisms that preserve harmonic functions and biharmonic functions respectively. In this paper, we introduce the notion of k-polyharmonic morphisms as maps that preserves polyharmonic functions of order k. For k = 3, we obtain several characterizations of triharmonic morphisms. We also give some relationships among harmonic, biharmonic, and triharmonic morphisms, and a relationship between triharmonic morphisms and p-harmonic morphisms.read more
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Complex-valued (p,q)-harmonic morphisms from Riemannian manifolds
TL;DR: The notion of (p, q)-harmonic morphisms between Riemannian manifolds was introduced in this article, which unifies several theories that have been studied during the last decades.
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Complex-valued (p,q)-harmonic morphisms from Riemannian manifolds
TL;DR: The notion of (p, q)-harmonic morphisms between Riemannian manifolds was introduced in this article, which unifies several theories that have been studied during the last decades.
References
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MonographDOI
Selected Topics in Harmonic Maps
James Eells,Luc Lemaire +1 more
TL;DR: In this article, the authors present a bibliography for differential geometric aspects of harmonic maps and problems relating to harmonic maps, as well as a supplementary bibliography with more details.
MonographDOI
Harmonic morphisms between Riemannian manifolds
Paul Baird,John C. Wood +1 more
TL;DR: In this article, the authors introduce complex-valued harmonic morphisms on three-dimensional Euclidean space and define polynomials to define harmonic mappings between Riemannian manifolds.
2-harmonic maps and their first and second variational formulas
TL;DR: In this paper, the authors study the case k = 2 and derive the first and second variational formulas of the 2-harmonic maps, give nontrivial examples of 2-harmonic maps and give proofs of nonexistence theorems of stable 2-mappings.
Journal ArticleDOI
Harmonic morphisms between riemannian manifolds
TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.org/conditions) are defined, i.e., toute utilisation commerciale ou impression systématique is constitutive d'une infraction pénale.