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2013•arXiv (Cornell University)Open access

Slant Ruled Surfaces in the Euclidean 3-space

Mehmet Önder

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Abstract

In this study, we define some new types of ruled surfaces called slant ruled surfaces when the angle between the Frenet vectors of the surface and a fixed direction is constant. We give some characterizations for a regular ruled surface to be a slant ruled surface in . Moreover, we obtain some corollaries which give the relationships between a slant ruled surface and its striction line.

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What this paper is about

In this study, we define some new types of ruled surfaces called slant ruled surfaces when the angle between the Frenet vectors of the surface and a fixed direction is constant. We give some characterizations for a regular ruled surface to be a slant ruled surface in . Moreover, we obtain some corollaries which give the relationships between a slant ruled surface and its striction line.

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Available abstract

In this study, we define some new types of ruled surfaces called slant ruled surfaces when the angle between the Frenet vectors of the surface and a fixed direction is constant. We give some characterizations for a regular ruled surface to be a slant ruled surface in . Moreover, we obtain some corollaries which give the relationships between a slant ruled surface and its striction line.

Key concepts: Frenet–Serret formulas, Ruled surface, Surface (topology), Euclidean geometry, Space (punctuation), Mathematics, Constant (computer programming), Line (geometry)

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