SURFACE FAMILIES WITH COMMON MANNHEIM-B CURVATURE LINE

Author:

SAFFAK ATALAY GÜLNUR1,MURAT HASRET2

Affiliation:

1. University of Ondokuz Mayıs, Department of Mathematics Education, 55270 Samsun, Turkey

2. University of Ondokuz Mayıs, Postgraduate Education Institute, 55270 Samsun, Turkey.

Abstract

In this study, we obtain necessary and sufficient conditions for the Mannheim B curve pair of the curve given by the Bishop frame in to be both parametric and curvature lines on the surface given by its parametric equation. Then, the same situation was expressed in the case of a ruled surface, which is a special and important type of surface, and the conditions for developable it among these surfaces were examined. Finally, examples supporting the study were given through the Maple15 program.

Publisher

Valahia University of Targoviste - Journal of Science and Arts

Reference37 articles.

1. Weatherburn, G.E., Differential Geometry of Three Dimensions, Cambridge at the University Press, 1955.

2. Willmore, T.J., An Introduction to Differential Geometry, Delhi, India: Oxford University Press, 1959.

3. Struik, D.J., Lectures on Classical Differential Geometry: Second Edition, Addison- Wesley Publishing Co., Massachusetts, 1961

4. O’Neill, B., Elementary Differential Geometry. New York, NY, USA: Academic Press Inc., 1966.

5. Lipschutz, M.M., Theory and Problems Of Differential Geometry, New York, St. Louis, San Francisco, Toronto, Sydney, 1969.

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