Conformal Riemannian Maps between Riemannian Manifolds, Their Harmonicity and Decomposition Theorems

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dc.authoridSahin, Bayram/0000-0002-9372-1151
dc.authorwosidSahin, Bayram/AAG-7872-2021
dc.contributor.authorSahin, Bayram
dc.date.accessioned2024-08-04T20:32:21Z
dc.date.available2024-08-04T20:32:21Z
dc.date.issued2010
dc.departmentİnönü Üniversitesien_US
dc.description.abstractRiemannian maps were introduced by Fischer (Contemp. Math. 132: 331-366, 1992) as a generalization isometric immersions and Riemannian submersions. He showed that such maps could be used to solve the generalized eikonal equation and to build a quantum model. On the other hand, horizontally conformal maps were defined by Fuglede (Ann. Inst. Fourier (Grenoble) 28: 107-144, 1978) and Ishihara (J. Math. Kyoto Univ. 19: 215229, 1979) and these maps are useful for characterization of harmonic morphisms. Horizontally conformal maps (conformal maps) have their applications in medical imaging (brain imaging) and computer graphics. In this paper, as a generalization of Riemannian maps and horizontally conformal submersions, we introduce conformal Riemannian maps, present examples and characterizations. We show that an application of conformal Riemannian maps can be made in weakening the horizontal conformal version of Hermann's theorem obtained by Okrut (Math. Notes 66(1): 94-104, 1999). We also give a geometric characterization of harmonic conformal Riemannian maps and obtain decomposition theorems by using the existence of conformal Riemannian maps.en_US
dc.identifier.doi10.1007/s10440-008-9348-6
dc.identifier.endpage847en_US
dc.identifier.issn0167-8019
dc.identifier.issn1572-9036
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-77949269603en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage829en_US
dc.identifier.urihttps://doi.org/10.1007/s10440-008-9348-6
dc.identifier.urihttps://hdl.handle.net/11616/95001
dc.identifier.volume109en_US
dc.identifier.wosWOS:000274844900011en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.relation.ispartofActa Applicandae Mathematicaeen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectIsometric immersionen_US
dc.subjectRiemannian submersionen_US
dc.subjectHorizontally conformal submersionen_US
dc.subjectRiemannian mapen_US
dc.subjectConformal Riemannian mapen_US
dc.titleConformal Riemannian Maps between Riemannian Manifolds, Their Harmonicity and Decomposition Theoremsen_US
dc.typeArticleen_US

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