Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 2, pp. 615-635 (2004)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Lines of curvature, ridges and conformal invariants of hypersurfaces

M. C. Romero-Fuster and E. Sanabria-Codesal

Departament de Geometria i Topologia, Universitat de València, Spain, e-mail:; Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Spain, e-mail:

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.

Full text of the article:

Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.

© 2004 Heldermann Verlag
© 2004--2006 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition