Right Convexity

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