arXiv subjects

Bazanfare Mahaman

Publications and source records attributed to Bazanfare Mahaman.

2 recordsLinked to original sources

arXiv2008

Topology of Manifolds with Asymptotically Nonnegative Ricci Curvature

In this paper, we study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature. We show that a complete noncompact manifold with asymptoticaly nonnegative Ricci curvature and sectional curvature decay at most quadratically is diffeomorphic to a Euclidean n-space R^n under some conditions on the density of rays starting from the base point p or on the volume growth of geodesic balls in M.

math.DG↗

arXiv2004

Sphere Theorem for Manifolds with Positive Curvature

In this paper, we prove that, for any integer $n\ge 2,$ there exists an $ε_{n} \ge 0$ so that if $M$ is an n-dimensional complete manifold with sectional curvature $ K_{M}\ge 1$ and if $M$ has conjugate radius bigger than $\fracπ{2} $ and contains a geodesic loop of length $2(π-ε_{n}),$ then $M$ is diffeomorphic to the Euclidian unit sphere $S^{n}.$

math.DG↗