On the geometry and topology of manifolds of positive bi-Ricci curvature

Abstract

We introduce some new curvature quantities such as conformal Ricci curvature and bi-Ricci curvature and extend the classical Myers theorem under these new curvature conditions. Moreover, we are able to obtain the Myers type theorem for minimal submanifolds in ambient manifolds with positive bi-Ricci curvature. Some topological applications are discussed. We also give examples of manifolds of positive bi-Ricci curvature and prove that the connect sum of manifolds of positive bi-Ricci curvature admits metrics of positive bi-Ricci curvature.