The nonlinear scalar-field realisation of w 1+∞ symmetry in d = 2 dimensions is studied in analogy to the nonlinear realisation of d = 4 conformal symmetry SO(4, 2). The w 1+∞ realisation is derived from a coset-space construction in which the divisor group is generated by the non-negative modes of the Virasoro algebra, with subsequent application of an infinite set of co-variant constraints. T...

I discuss tree-level amplitudes in cubic topological string field theory, showing that a certain family of gauge conditions leads to an A∞ algebra of tree-level string products which define a potential describing the dynamics of physical states. Upon using results of modern deformation theory, I show that the string moduli space admits two equivalent descriptions, one given in standard Maurer-C...

Let G = ( R∗+ × SO0(1, n) ) n Rn+1 be the Weyl-Poincaré group and KAN be the Iwasawa decomposition of SO0(1, n) with K = SO(n). Then the “affine Weyl-Poincaré group” Ga = ( R∗+ × AN ) n Rn+1 can be realized as the complex tube domain Π = Rn+1 + iC or the classical Cartan domain BDI(q = 2). The square-integrable representations of G and Ga give the admissible wavelets and wavelet transforms. An ...

A hypersurface is said to be totally biharmonic if all its geodesics are curves in the ambient space. We prove that a into space form an isoparametric hypersurface, which allows us give full classification of hypersurfaces these spaces. Moreover, restricting ourselves 3-dimensional case, we show surfaces Bianchi–Cartan–Vranceanu spaces and their classification. In particular, that, leaving asid...

In this paper, differential invariants of null Cartan curves are studied in (n+2) dimensional Lorentzian similarity geometry. The fundamental theorem for a curve geometry is investigated and the characterization all self-similar parameterized by de Sitter parameter Minkowski space-time given.

Experimental observation of Majorana fermion matter gives a new impetus to the understanding of the Lorentz symmetry and its extension, the geometrical properties of the ambient space-time structure, matter–antimatter symmetry and some new ways to understand the baryo–genesis problem in cosmology. Based on the primordial Majorana fermion matter assumption, we discuss a possibility to solve the ...