CURVES IN n-DIMENSIONAL k-ISOTROPIC SPACE

Abstract

In this paper we develop the theory of curves in n-dimensional k-isotropic space I~. We derive explicit expressions and geometrical interpretations for the curvatures of a curve. In this paper we develop the theory of curves in I~. We construct the Frenet frame of an admissible curve and calculate the explicit expressions of the curvatures of such a curve. We derive also the geometrical interpretation of these curvatures and investigate the curves having some of their curvatures equal to zero. Finally we describe the conditions, in terms of curvatures, if a curve lies in an (-isotropic m-plane. Let A denote an n-dimensional affine space and V its corresponding vector space. The space V is decomposed in a direct sum