Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 48, No. 1, pp. 237250 (2007) 

A surface which has a family of geodesics of curvatureN. AndoFaculty of Science, Kumamoto University, 2391 Kurokami, Kumamoto 8608555, JapanAbstract: 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 Full text of the article:
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