Abstract:We study the asymptotic behavior of curvature and prove that the integral of curvature along a geodesic without conjugate points is nonpositive and some generalizations of Myers theorem and Cohn-Vossen's theorem. Some applications are also given.Key words: Riemannian manifold, geodesic, conjugate point.
MAIN RESULTSLet M n be an n-dimensional Riemannian manifold and let d(x, y) be the distance induced by the metric. (Ambrose 1957) showed that if the integral of the Ricci curvature along a geodesic γ : [0, +∞) … Show more
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