15,306 research outputs found
Topological and differentiable rigidity of submanifolds in space forms
Let be an -dimensional simply connected space form with
nonnegative constant curvature . We prove that if is a compact
submanifold in , and if where is the mean
curvature of , then is homeomorphic to a sphere. We also show that the
pinching condition above is sharp. Moreover, we obtain a new differentiable
sphere theorem for submanifolds with positive Ricci curvature.Comment: 12 page
Poisson Cohomology of Del Pezzo surfaces
In this note, we compute the Poisson cohomology groups for any Poisson Del
Pezzo surface
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