Harmonic morphisms and subharmonic functions.
Choi, Gundon, Yun, Gabjin (2005)
International Journal of Mathematics and Mathematical Sciences
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Choi, Gundon, Yun, Gabjin (2005)
International Journal of Mathematics and Mathematical Sciences
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Chiang, Yuan-Jen, Sun, Hongan (2001)
International Journal of Mathematics and Mathematical Sciences
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Todjihounde, Leonard (2006)
International Journal of Mathematics and Mathematical Sciences
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Yunhee Euh, Jeong Hyeong Park, Kouei Sekigawa (2017)
Czechoslovak Mathematical Journal
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We derive a curvature identity that holds on any 6-dimensional Riemannian manifold, from the Chern-Gauss-Bonnet theorem for a 6-dimensional closed Riemannian manifold. Moreover, some applications of the curvature identity are given. We also define a generalization of harmonic manifolds to study the Lichnerowicz conjecture for a harmonic manifold “a harmonic manifold is locally symmetric” and provide another proof of the Lichnerowicz conjecture refined by Ledger for the 4-dimensional...
A. Mohammed Cherif, Djaa Mustapha (2014)
Commentationes Mathematicae Universitatis Carolinae
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In this paper, we study the characterization of generalized -harmonic morphisms between Riemannian manifolds. We prove that a map between Riemannian manifolds is an -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],...
Wang, Ze-Ping (2009)
Beiträge zur Algebra und Geometrie
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Tsagas, Gr., Bitis, Gr. (2001)
Balkan Journal of Geometry and its Applications (BJGA)
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Bent Fuglede (1978)
Annales de l'institut Fourier
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A harmonic morphism between Riemannian manifolds and is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim dim, since otherwise every harmonic morphism is constant. It is shown that a harmonic morphism is the same as a harmonic mapping in the sense of Eells and Sampson with the further property of being semiconformal, that is, a conformal submersion of the points where vanishes. Every non-constant harmonic morphism is shown to be...
González-Dávila, J.C., Vanhecke, Lieven (1997)
Publications de l'Institut Mathématique. Nouvelle Série
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Anders Kock (2004)
Open Mathematics
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We describe for any Riemannian manifold M a certain scheme M L, lying in between the first and second neighbourhood of the diagonal of M. Semi-conformal maps between Riemannian manifolds are then analyzed as those maps that preserve M L; harmonic maps are analyzed as those that preserve the (Levi-Civita-) mirror image formation inside M L.