On Extensions of Myers' Theorem |
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Authors: | Li Xue-Mei |
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Affiliation: | Mathematics Institute, University of Warwick Coventry CV4 7AL |
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Abstract: | Let M be a compact Riemannian manifold, and let h be a smoothfunction on M. Let ph(x) = inf| |1(Ricx( , )2Hess(hx( , )).Here Ricx denotes the Ricci curvature at x and Hess(h) is theHessian of h. Then M has finite fundamental group if hph<0. Here h =: +2L h is the Bismut-Witten Laplacian. This leadsto a quick proof of recent results on extension of Myers' theoremto manifolds with mostly positive curvature. There is also asimilar result for noncompact manifolds. |
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