Yamabe flow and the Myers-type theorem on complete manifolds

Details Yamabe flow and the Myers-type theorem on complete manifolds Yamabe flow and the Myers-type theorem on complete manifolds

2010-03-20

arxiv.org/abs/1003.3914v4

Mathematics

Differential Geometry

21 pages

Scientific paper

In this paper,we prove the following Myers-type theorem: if $(M^n,g)$, $n\geq
3$, is an n-dimensional complete locally conformally flat Riemannian manifold
with bounded Ricci curvature satisfying the Ricci pinching condition $Rc\geq
\epsilon Rg>0$, where $\epsilon>0$ is an uniform constant, then $M^n$ must be
compact.

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