Introduction Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly realcompact spaces Extensions and liftings of mappings Infinite dimensional… Expand

I. Manifolds and Lie Groups.- II. Differential Forms.- III. Bundles and Connections.- IV. Jets and Natural Bundles.- V. Finite Order Theorems.- VI. Methods for Finding Natural Operators.- VII.… Expand

We study some Riemannian metrics on the space of regular smooth curves in the plane, viewed as the orbit space of maps from the circle to the plane modulo the group of diffeomorphisms of the circle,… Expand

The L 2 -metric or Fubini-Study metric on the non-linear Grassmannian of all submanifolds of type M in a Riemannian man- ifold (N;g) induces geodesic distance 0. We discuss another metric which… Expand

Manifolds and vector fields Lie groups and group actions Differential forms and de Rham cohomology Bundles and connections Riemann manifolds Isometric group actions or Riemann $G$-manifolds… Expand

This paper studies a specific metric on plane curves that has the property of being isometric to classical manifold (sphere, complex projective, Stiefel, Grassmann) modulo change of parametrization,… Expand