Asymptotics of curvature in a space of positive curvature

RICCI CURVATURE OF SUBMANIFOLDS OF A SASAKIAN SPACE FORM

Involving the Ricci curvature and the squared mean curvature, we obtain basic inequalities for different kind of submaniforlds of a Sasakian space form tangent to the structure vector field of the ambient manifold. Contrary to already known results, we find a different necessary and sufficient condition for the equality for Ricci curvature of C-totally real submanifolds of a Sasakian space form...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Global Behavior of Curves in a Space of Positive Curvature

It is well known that any geodesic in a complete noncompact space of positive curvature goes to infinity. In this paper, we prove that this is true for more general curves and estimate how fast they go to infinity in terms of their curvature and curvature of the space. 0. Introduction. 0.1. All manifolds, submanifolds and curves here are assumed to be of class C°°. A curve parametrized by its a...

Curvature Estimates in Asymptotically At Manifolds of Positive Scalar Curvature

Curvature Estimates in Asymptotically Flat Manifolds of Positive Scalar Curvature

Suppose that (Mn, g) is an asymptotically flat Riemannian spin manifold of positive scalar curvature. The positive mass theorem [1, 2, 3] states that the total mass of the manifold is always positive, and is zero if and only if the manifold is flat. This result suggests that there should be an inequality which bounds the Riemann tensor in terms of the total mass and implies that curvature must ...