On extensions of Myers’ theorem
File(s)
Accepted version
Author(s)
Li, Xue-Mei
Type
Journal Article
Abstract
Let M be a compact Riemannian manifold, and let h be a smooth function on M. Let ph(x) = inf|υ|−1(Ricx(υ,υ)−2Hess(hx(υ,υ)). Here Ricx denotes the Ricci curvature at x and Hess(h) is the Hessian of h. Then M has finite fundamental group if Δh−ph <0. Here Δh =:Δ+2L∇h is the Bismut-Witten Laplacian. This leads to a quick proof of recent results on extension of Myers' theorem to manifolds with mostly positive curvature. There is also a similar result for noncompact manifolds.
Date Issued
1995
Citation
The Bulletin of the London Mathematical Society, 1995, 27, pp.392-396
ISSN
0024-6093
Start Page
392
End Page
396
Journal / Book Title
The Bulletin of the London Mathematical Society
Volume
27
Copyright Statement
© 1995 London Mathematical Society
Identifier
http://dx.doi.org/10.1112/blms/27.4.392
Subjects
0101 Pure Mathematics
General Mathematics
Notes
mrclass: 58G32 (53C20) mrnumber: 1335292 mrreviewer: Ming Liao
Article Number
4