E. E. Levi convexity and the Hans Lewy problem. Part I : reduction to vanishing theorems
Necessary and sufficient conditions for local embeddability of abstract structures are expressed in terms of the commutation of the vector fields with a complex Lie algebra. These results extend to more general systems.
We formulate the equivalence problem, in the sense of É. Cartan, for families of minimal rational curves on uniruled projective manifolds. An important invariant of this equivalence problem is the variety of minimal rational tangents. We study the case when varieties of minimal rational tangents at general points form an isotrivial family. The main question in this case is for which projective variety , a family of minimal rational curves with -isotrivial varieties of minimal rational tangents...
Given a differentiable action of a compact Lie group G on a compact smooth manifold V , there exists [3] a closed embedding of V into a finite-dimensional real vector space E so that the action of G on V may be extended to a differentiable linear action (a linear representation) of G on E. We prove an analogous equivariant embedding theorem for compact differentiable spaces (∞-standard in the sense of [6, 7, 8]).