Bertrand and Mannheim Partner -curves on Parallel Surfaces

Abstract

In this paper we study Bertrand and Mannheim partner -curves on parallel surface. Using the definition of parallel surfaces, first we find images of two curves lying on two different surfaces and satisfying the conditions to be Bertrand partner -curve or Mannheim partner -curve. Then we obtain relationships between Bertrand and Mannheim partner -curves and their image curves.

Keywords

• Parallel surface
• Bertrand partner -curves
• Mannheim partner -curves.