Curvature Groups of a Hypersurface

Samuel I. Goldberg
1976 Proceedings of the American Mathematical Society  
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^ replaced by a sheaf of harmonic vector fields. If the Ricci tensor is nondegenerate the HP(M) vanish. If
more » ... he HP(M) vanish. If Sj, # 0, and there are no parallel vector fields, locally, the HP(M) are isomorphic with the corresponding de Rham groups.
doi:10.2307/2040799 fatcat:om5bhtriwner7mzji7drboymr4