Geodesics and Almost Geodesics Curves

Abstract

We determine in $$\mathbb {R}^n$$ the form of curves $$\mathcal C$$ for which also any image under an $$(n-1)$$ -dimensional algebraic torus is a geodesic or an almost geodesic with respect to an affine connections $$\nabla $$ with constant coefficients and calculate explicitly the components of $$\nabla $$ . In this paper we consider the special case for the connection $$\nabla $$ when any curve from a set of images of $$\mathcal C$$ is almost geodesic with respect to $$\nabla $$ .