Right Convexity

A convex set is F-convex if every pair of points in the set lie in a right triangle included in the set. We characterize F-convex sets, find some classes of F-convex sets, investigate F-convexity for cones and cylinders, and find out that most convex bodies are F-convex. On our way, we also describe the curvature at the endpoints of diameters of most convex bodies