It is shown the existence of an uncountable infinity of asymptotic structures (i.e. equivalence's classes of quasi-isometric riemannian metrics) on the conformal class of the hyperbolic plan .
In this paper, we determine a class of possible restricted holonomy groups for a non-irreducible indecomposable pseudoriemannian manifold with signature (2,2 + n). In particular, we deduce that which associated to symmetric spaces; and give some examples of such spaces. Finally, we construct some examples of metrics whose restricted holonomy groups are not closed.
On montre que sur toute variété de dimension 3 compacte orientable munie d’une action libre de , il existe une forme de contact invariante induisant une 1-forme invariante donnée sur une surface invariante de , si et seulement si et ne s’annulent pas simultanément.
We generalize the spinorial characterization of isometric immersions of surfaces in given by T. Friedrich to surfaces in and . The main argument is the interpretation of the energy-momentum tensor associated with a special spinor field as a second fundamental form. It turns out that such a characterization of isometric immersions in terms of a special section of the spinor bundle also holds in the case of hypersurfaces in the Euclidean -space.