Vector fields and modified Ricci curvatures
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The classical Bochner theorem says that on a closed Riemannian mani-fold of negative Ricci curvature there exists no non-trivial Killing vector ¯eld. This result raises a natural and more general problem. Can we weaken the hypothesis on the Ricci curvature? In the present paper we consider the notion of ¸-automorphisms. Killing, a±ne, conformal, projective and Jacobi vector ¯elds are examples of ¸-automorphisms. Related to this problem, we give extensions of Bochner's vanish-ing theorems for the original Ricci curvature on a closed Riemannian manifold via modi¯ed Ricci curvatures in a uni¯ed way.
Abstract
The classical Bochner theorem says that on a closed Riemannian mani-fold of negative Ricci curvature there exists no non-trivial Killing vector ¯eld. This result raises a natural and more general problem. Can we weaken the hypothesis on the Ricci curvature? In the present paper we consider the notion of ¸-automorphisms. Killing, a±ne, conformal, projective and Jacobi vector ¯elds are examples of ¸-automorphisms. Related to this problem, we give extensions of Bochner's vanish-ing theorems for the original Ricci curvature on a closed Riemannian manifold via modi¯ed Ricci curvatures in a uni¯ed way.
참고문헌 (12)
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