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On Extensions of Myers' Theorem
Author(s) -
Li XueMei
Publication year - 1995
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/27.4.392
Subject(s) - mathematics , ricci curvature , pure mathematics , hessian matrix , extension (predicate logic) , manifold (fluid mechanics) , curvature , laplace operator , riemannian manifold , function (biology) , riemann curvature tensor , mathematical analysis , geometry , mechanical engineering , evolutionary biology , computer science , engineering , biology , programming language
Let M be a compact Riemannian manifold, and let h be a smooth function on M . Let p h ( x ) = inf|υ|− 1 (Ric x (υ,υ)−2Hess( h x (υ,υ)). Here Ric x denotes the Ricci curvature at x and Hess( h ) is the Hessian of h . Then M has finite fundamental group if Δ h − p h <0. Here Δ h =:Δ+2 L ∇ 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.