ON AHLFORS' IMAGINARY SCHWARZIAN

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dc.contributor.authorChuaqui, Martin
dc.date.accessioned2025-01-20T23:55:42Z
dc.date.available2025-01-20T23:55:42Z
dc.date.issued2021
dc.description.abstractWe study geometric aspects of the imaginary Schwarzian S2f for curves in 3-space, as introduced by Ahlfors in [1]. We show that S2f points in the direction from the center of the osculating sphere to the point of contact with the curve. We also establish an important law of transformation of S2f under Mobius transformations. We finally study questions of existence and uniqueness up to Mobius transformations of curves with given real and imaginary Schwarzians. We show that curves with the same generic imaginary Schwarzian are equal provided they agree to second order at one point, while prescribing in addition the real Schwarzian becomes an overdetermined problem.
dc.fuente.origenWOS
dc.identifier.doi10.5186/aasfm.2021.4628
dc.identifier.eissn2737-114X
dc.identifier.issn2737-0690
dc.identifier.urihttps://doi.org/10.5186/aasfm.2021.4628
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/95105
dc.identifier.wosidWOS:001107525700019
dc.issue.numero1
dc.language.isoen
dc.pagina.final353
dc.pagina.inicio345
dc.revistaAnnales fennici mathematici
dc.rightsacceso restringido
dc.subjectAhlfors' Schwarzian for curves
dc.subjectimaginary Schwarzian
dc.subjectosculating sphere
dc.subjectMobius transformation
dc.subjectoverdetermined problem
dc.titleON AHLFORS' IMAGINARY SCHWARZIAN
dc.typeartículo
dc.volumen46
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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