Mapping 2-D defects in a conductive half-space by eigenfunction expansions in K-space of Fourier-Laplace transforms

info:eu-repo/semantics/published

The Euroregional discourse. Increasing evidence towards legitimizing an institutional space

From a multilingual corpus composed of institutional websites published by the Euroregions, this article attempts to explore the discursive indications which tend to legitimize the notion of Euroregional space. The lexicometric and qualitative observations lead to a compliance to the normative objectives of the European politics and to the standardization of the euroregional representations, in spite of languages and issuing cross-border areas.

Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms

The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel.