Grove and Shiohama used the critical point theory of a distance function to prove the diameter sphere theorem. In light of the angular distribution of minimizing geodesics, we examine and develop the techniques in its proof to make some diameter sphere theorems and study complete noncompact manifolds, using a generalized Toponogov comparison theorem.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.