On generalized f -harmonic morphisms

A. Mohammed Cherif; Djaa Mustapha

Commentationes Mathematicae Universitatis Carolinae (2014)

  • Volume: 55, Issue: 1, page 17-27
  • ISSN: 0010-2628

Abstract

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In this paper, we study the characterization of generalized f -harmonic morphisms between Riemannian manifolds. We prove that a map between Riemannian manifolds is an f -harmonic morphism if and only if it is a horizontally weakly conformal map satisfying some further conditions. We present new properties generalizing Fuglede-Ishihara characterization for harmonic morphisms ([Fuglede B., Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble) 28 (1978), 107–144], [Ishihara T., A mapping of Riemannian manifolds which preserves harmonic functions, J. Math. Kyoto Univ. 19 (1979), no. 2, 215–229]).

How to cite

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Cherif, A. Mohammed, and Mustapha, Djaa. "On generalized $f$-harmonic morphisms." Commentationes Mathematicae Universitatis Carolinae 55.1 (2014): 17-27. <http://eudml.org/doc/260801>.

@article{Cherif2014,
abstract = {In this paper, we study the characterization of generalized $f$-harmonic morphisms between Riemannian manifolds. We prove that a map between Riemannian manifolds is an $f$-harmonic morphism if and only if it is a horizontally weakly conformal map satisfying some further conditions. We present new properties generalizing Fuglede-Ishihara characterization for harmonic morphisms ([Fuglede B., Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble) 28 (1978), 107–144], [Ishihara T., A mapping of Riemannian manifolds which preserves harmonic functions, J. Math. Kyoto Univ. 19 (1979), no. 2, 215–229]).},
author = {Cherif, A. Mohammed, Mustapha, Djaa},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$f$-harmonic morphisms; $f$-harmonic maps; horizontally weakly conformal map; -harmonic morphism; -harmonic map; horizontally weakly conformal map},
language = {eng},
number = {1},
pages = {17-27},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On generalized $f$-harmonic morphisms},
url = {http://eudml.org/doc/260801},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Cherif, A. Mohammed
AU - Mustapha, Djaa
TI - On generalized $f$-harmonic morphisms
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 1
SP - 17
EP - 27
AB - In this paper, we study the characterization of generalized $f$-harmonic morphisms between Riemannian manifolds. We prove that a map between Riemannian manifolds is an $f$-harmonic morphism if and only if it is a horizontally weakly conformal map satisfying some further conditions. We present new properties generalizing Fuglede-Ishihara characterization for harmonic morphisms ([Fuglede B., Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble) 28 (1978), 107–144], [Ishihara T., A mapping of Riemannian manifolds which preserves harmonic functions, J. Math. Kyoto Univ. 19 (1979), no. 2, 215–229]).
LA - eng
KW - $f$-harmonic morphisms; $f$-harmonic maps; horizontally weakly conformal map; -harmonic morphism; -harmonic map; horizontally weakly conformal map
UR - http://eudml.org/doc/260801
ER -

References

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  2. Baird P., Wood J.C., Harmonic Morphisms between Riemannain Manifolds, Clarendon Press, Oxford, 2003. MR2044031
  3. Course N., f-harmonic maps which map the boundary of the domain to one point in the target, New York J. Math. 13 (2007), 423–435 (electronic). Zbl1202.58012MR2357720
  4. Djaa M., Cherif A.M., Zegga K., Ouakkas S., On the generalized of harmonic and bi-harmonic maps, Int. Electron. J. Geom. 5 (2012), no. 1, 90–100. MR2915490
  5. Mustapha D., Cherif A.M., On the generalized f -biharmonic maps and stress f -bienergy tensor, Journal of Geometry and Symmetry in Physics, JGSP 29 (2013), 65–81. MR3113559
  6. Fuglede B., 10.5802/aif.691, Ann. Inst. Fourier (Grenoble) 28 (1978), 107–144. Zbl0408.31011MR0499588DOI10.5802/aif.691
  7. Gudmundsson S., The geometry of harmonic morphisms, University of Leeds, Department of Pure Mathematics, April 1992. Zbl0715.53029
  8. Ishihara T., A mapping of Riemannian manifolds which preserves harmonic functions, J. Math. Kyoto Univ. 19 (1979), no. 2, 215–229. Zbl0421.31006MR0545705
  9. Lichnerowicz A., Applications harmoniques et variétés Kähleriennes, 1968/1969 Symposia Mathematica, Vol. III (INDAM, Rome, 1968/69), pp. 341–402, Academic Press, London. Zbl0193.50101MR0262993
  10. Ou Y.L., On f -harmonic morphisms between Riemannian manifolds, arxiv:1103.5687, Chinese Ann. Math., series B(to appear). 
  11. Ouakkas S., Nasri R., Djaa M., On the f-harmonic and f-biharmonic maps, JP J. Geom. Topol. 10 (2010), no. 1, 11–27. Zbl1209.58014MR2677559

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