Curvature groups of a hypersurface

Curvature Groups of a Hypersurface

A cochain complex associated with the vector 1-form determined by the first and second fundamental tensors of a hypersurface M in E"+l is introduced. Its cohomology groups HP(M), called curvature groups, are isomorphic with the cohomology groups of M with coefficients in a subsheaf %R of the sheaf S of closed vector fields on M. If M is a minimal variety, the same conclusion is valid with S^ re...

Curvature of a Closed Hypersurface

Ricci Curvature Decay near a Real Hypersurface Singularity

Hypersurface complements , Milnor fibers and higher homotopy groups of arrangments

The decay of the Ricci curvature at a real hypersurface singularity

The Ricci curvature at an isolated singularity of an immersed hypersurface exhibits a local behaviour echoing a global property of the Ricci curvature on a complete hypersurface in euclidean space (i.e., the Efimov theorem [12], that sup Ric ≥ 0). This local behaviour takes the form of a near universal bound on the decay of the Ricci curvature at a simple singularity (eg. a cone singularity) in...