Ricci curvature and volume growth
نویسندگان
چکیده
منابع مشابه
Volume Geodesic Distortion and Ricci Curvature for Hamiltonian Dynamics
We study the variation of a smooth volume form along extremals of a variational problem with nonholonomic constraints and an action-like Lagrangian. We introduce a new invariant describing the interaction of the volume with the dynamics and we study its basic properties. We then show how this invariant, together with curvature-like invariants of the dynamics introduced in [4], appear in the exp...
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We study the variation of a smooth volume form along extremals of a variational problem with nonholonomic constraints and an action-like Lagrangian. We introduce a new invariant describing the interaction of the volume with the dynamics and we study its basic properties. We then show how this invariant, together with curvature-like invariants of the dynamics introduced in [4], appear in the exp...
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10. In this note we consider complete Riemannian manifolds with Ricci curvature bounded from below. The well-known theorems of Myers and Bishop imply that a manifold M n with Ric ~ n 1 satisfies diam(1l1n) ~ diam(Sn(I)), Vol(Mn) ~ Vol(Sn(I)). It follows from [Ch] that equality in either of these estimates can be achieved only if M n is isometric to Sn (1). The natural conjecture is that a manif...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1991
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1991.148.161