Geodesically reversible Finsler 2-spheres of constant curvature

A Finsler space is said to be geodesically reversible if each oriented geodesic can be reparametrized as a geodesic with the reverse orientation. A reversible Finsler space is geodesically reversible, but the converse need not be true. In this note, building on recent work of LeBrun and Mason, it is shown that a geodesically reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily projectively flat. As a corollary, using a previous result of the author, it is shown that a reversible Finsler metric of constant flag curvature on the 2-sphere is necessarily a Riemannian metric of constant Gauss curvature, thus settling a long- standing problem in Finsler geometry.

Makarios Now: Plundering Athens and Hippo

A Christian doctrine of happiness differs greatly from contemporary and pseudo-Christian conceptions of happiness, which are measured subjectively and by the accumulation of external goods. In order to develop a fresh account with objective standards, I critique, integrate and revise Aristotle and Augustine’s accounts of happiness. Additionally, I rely heavily on scriptures to present a telos of godlikeness that in turn informs a robust account of makarios. Throughout the thesis, the argument is made that happiness (eudaimonia) and blessedness (makarios) are equivalents. Despite the skepticism of liberal theologians, Christian happiness (makarios) is promised in the New Testament and achievable in this life. Fundamentally, makarios is relational, active, constant, and dependent.