IJPAM: Volume 69, No. 1 (2011)

RULED SURFACES AS A TANGENT DEVELOPABLE
IN POSITIVE CHARACTERISTIC AND
OSCULATING PLANES TO A SUBCURVE OF THEM

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract. Let $Y\subset \mathbb {P}^n$ be an integral curve contained in a surface $S$. When is the osculating plane of $Y$ at a general $P\in Y$ equal to the tangent plane of $S$ at $P$? In positive characteristic we find for each ruled surface $S$ a curve $Y$ as above and classify all such $Y$ if $S$ is either a smooth quadric or a cone.

Received: January 11, 2011

AMS Subject Classification: 14H50, 14N05

Key Words and Phrases: strange curve, tangent developable, osculating space

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 1