CURVATURE BUNDLE MORPHISMS FOR HYPERSURFACE GENERALIZED DIRAC OPERATORS

The datum of a generalized Dirac operator (D) over bar (in the sense of Gromov and Lawson) on a Riemannian manifold (M) over bar can be restricted to a hypersurface M subset of (K) over bar, then suitably altered via a bundle morphism-valued one-form Omega on M, commuting with Clifford multiplication, to yield a generalized Dirac operator D on M. How do the curvature bundle morphisms (R) over bar (vertical bar M) and R associated to (D) over bar and D relate? The Gauss-like relationship we are going to establish in this paper involves the shape operator A of M, a normal part of the curvature associated to the connection of (D) over bar, and the curvature of the form Omega. Applications are then given to operators of Spin and Clifford type.