Many interesting geometric structures on manifolds can be interpreted as structures locally modelled on homogeneous spaces. Given a homogeneous space (X,G) and a manifold M , there is a deformation space of structures on M locally modelled on the geometry of X invariant under G. Such a geometric structure on a manifold M determines a representation (unique up to inner automorphism) of the funda...

Abstract Let f : X ? ? {f:X\rightarrow\mathbb{R}} be a function defined on connected nonsingular real algebraic set X in n {\mathbb{R}^{n}} . We prove that regularity of f can detected by controlling the restrictions ...