Finiteness Of Fundamental Groups Research Articles

On curvatures and fundamental groups of Finslermanifolds

Finsler manifolds aredifferentiable manifolds equipped with Riemannian metrics withoutthe quadratic restriction. In this paper, some recent developmentsand new results on curvatures and fundamental groups of Finslermanifolds are summarized briefly. The contents contain the growth offundamental groups, the entropy of manifolds and fundamental groups,the first Betti number and the finiteness of fundamental groups.

Ricci curvature of spacelike hypersurfaces in de Sitter space

In this paper, we study the spacelike hypersurfaces in de Sitter space S1n+1(c), and give some estimates on the Ricci curvature tensor and the square of its length. By these estimates, many properties of spacelike hypersurfaces are derived, that is, the compactness and convexity of spacelike hypersurfaces, the finiteness of fundamental group. We also get an integral inequality on eigenvalue of the Laplacian operator and a sufficient and necessary condition for such hypersurfaces to be totally geodesic.

Bounds on the fundamental groups with integral curvature bound

We extend the polynomial growth of the fundamental group, the first Betti number estimate and finiteness of fundamental groups of compact Riemannian manifolds from pointwise Ricci lower bound to integral Ricci lower bound, using a volume comparison for star-shaped domains.