Differentiable maps into riemannian manifolds of constant stable osculating rank. II. (Frenet-Theory).
Groping our way toward a theory of singular spaces with positive scalar curvatures we look at the Dirac operator and a generalized Plateau problem in Riemannian manifolds with corners. Using these, we prove that the set of C 2-smooth Riemannian metrics g on a smooth manifold X, such that scalg(x) ≥ κ(x), is closed under C 0-limits of Riemannian metrics for all continuous functions κ on X. Apart from that our progress is limited but we formulate many conjectures. All along, we emphasize geometry,...
In this paper some relation among the Dirac operator on a Riemannian spin-manifold , its projection on some embedded hypersurface and the Dirac operator on with respect to the induced (called standard) spin structure are given.