Affine curvature of plane geodesic lines on affine hypersurfaces - Shuhaylo, O. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
We establish a necessary and sufficient condition for a geodesic line on a nondegenerate hypersurface to be a plane curve.We deduce a formula for the affine curvature of a plane geodesic line on the affine hypersurface in terms of the affinefundamental form and the shape operator. We present the definition of transverse curvature and determine some of itselementary properties.