TITLE:
Manifolds with Bakry-Emery Ricci Curvature Bounded Below
AUTHORS:
Issa Allassane Kaboye, Bazanfaré Mahaman
KEYWORDS:
Bakry Émery Ricci Curvature, Myers Theorem, Volume Comparison Theorem, Topological Rigidity Theorem
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.6 No.11,
October
17,
2016
ABSTRACT: 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.