arXiv subjects

Alice Lim

Publications and source records attributed to Alice Lim.

2 recordsLinked to original sources

arXiv2020

Locally Homogeneous Non-gradient Quasi-Einstein 3-Manifolds

In this paper, we classify the compact locally homogeneous non-gradient $m$-quasi Einstein 3-manifolds. Along the way, we prove that given a compact quotient of a Lie group of any dimension that is $m$-quasi Einstein, the potential vector field $X$ must be left invariant and Killing. We also classify the nontrivial $m$-quasi Einstein metrics that are a compact quotient of be the product of two Einstein metrics. We also show that $S^1$ is the only compact manifold of any dimension which admits a metric which is nontrivially $m$-quasi Einstein and Einstein.

math.DG↗

arXiv2020

The Splitting Theorem and Topology of Noncompact Spaces with Nonnegative N-Bakry \'Emery Ricci Curvature

In this paper, we generalize topological results known for noncompact manifolds with nonnegative Ricci curvature to spaces with nonnegative $N$-Bakry \'Emery Ricci curvature. We study the Splitting Theorem and a property called the geodesic loops to infinity property in relation to spaces with nonnegative $N$-Bakry \'Emery Ricci Curvature. In addition, we show that if $M^n$ is a complete, noncompact Riemannian manifold with nonnegative $N$-Bakry \'Emery Ricci curvature where $N>n$, then $H_{n-1}(M,\mathbb{Z})$ is $0$.

math.DG↗