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In Riemannian geometry,there is a well-known theorem called Lichnorwicz and Obata theorem: Let (Mn,g) be a compact,complete Rie-mannian manifold satisfying Ric ≥ (n-1)K for some positive constant K.Then the first positive eigenvalue of Laplace-Beltrami operator λ1 ≥ nK and the equality holds if and only if M is iso-metric to the sphere Sn of radius 1/√.