Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 45, No. 2, pp. 615-635 (2004)
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Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 2, pp. 615-635 (2004) |
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Lines of curvature, ridges and conformal invariants of hypersurfacesM. C. Romero-Fuster and E. Sanabria-CodesalDepartament de Geometria i Topologia, Universitat de València, Spain, e-mail: romeromc@post.uv.es; Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Spain, e-mail: esanabri@mat.upv.esAbstract: We define some conformally invariant differential 1-forms along the curvature lines of a hypersurface $M$ and we observe that the ridges of $M$ can be viewed as their zeros. We characterize the highest order ridges, which are isolated points generically, as zeros of these conformally invariant differential 1-forms along special curves of ridges. We also prove that the highest order ridges are vertices of the curvature lines when they are considered as curves in $n$-space. Full text of the article:
Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.
© 2004 Heldermann Verlag
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