On extensions of Myers’ theorem

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Title: On extensions of Myers’ theorem
Authors: Li, X-M
Item 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.
Issue Date: 1-Jul-1995
URI: http://hdl.handle.net/10044/1/54083
DOI: https://dx.doi.org/10.1112/blms/27.4.392
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
Keywords: 0101 Pure Mathematics
General Mathematics
Notes: mrclass: 58G32 (53C20) mrnumber: 1335292 mrreviewer: Ming Liao
Article Number: 4
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences

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