Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 48, No. 1, pp. 237-250 (2007)

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A surface which has a family of geodesics of curvature

N. Ando

Faculty of Science, Kumamoto University, 2--39--1 Kurokami, Kumamoto 860--8555, Japan

Abstract: We will study a surface in \mbox{\boldmath{$R$}}$^3$ without any umbilical point such that the integral curves of some principal distribution are geodesics. In particular, the lines of curvature of such a surface will be characterized intrinsically and extrinsically: the semisurface structure of such a surface will be characterized in terms of local representation of the first fundamental form; the curvatures and the torsions of the lines of curvature as space curves will be characterized.

Classification (MSC2000): 53A05, 53A99, 53B25

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Electronic version published on: 14 May 2007. This page was last modified: 27 Jan 2010.

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