Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 2, pp. 615-635 (2004)
Lines of curvature, ridges and conformal invariants of hypersurfaces
M. C. Romero-Fuster and E. Sanabria-CodesalDepartament de Geometria i Topologia, Universitat de València, Spain, e-mail: email@example.com; Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Spain, e-mail: firstname.lastname@example.org
Abstract: 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.
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Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.