Author(s)

Issa Allassane Kaboye¹, Bazanfaré Mahaman²

¹Faculté de Sciences et Techniques, Université de Zinder, Zinder, Niger.
²Département de Mathématiques et Informatique, Université Abdou Moumouni, Niamey, Niger.

In this paper we show that, under some conditions, if M is a manifold with Bakry-émery Ricci curvature bounded below and with bounded potential function then M is compact. We also establish a volume comparison theorem for manifolds with nonnegative Bakry-émery Ricci curvature which allows us to prove a topolological rigidity theorem for such manifolds.

Bakry Émery Ricci Curvature, Myers Theorem, Volume Comparison Theorem, Topological Rigidity Theorem

Kaboye, I. and Mahaman, B. (2016) Manifolds with Bakry-Emery Ricci Curvature Bounded Below. Advances in Pure Mathematics, 6, 754-764. doi: 10.4236/apm.2016.611061.