Related papers: Bohr space in six dimensions
A relativistic 3-brane can be given a conformally invariant, gauge-type, formulation provided the embedding space is six-dimensional. The implementation of conformal invariance requires the use of a modified measure, independent of the…
We consider Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. We use the conformal algebra to build additional {\em quadratic} first integrals, thus constructing a large…
We put forward an idea that physical phenomena have to be treated in 5-dimensional space where the fifth coordinate is the interval S. Thus, we considered the (1+4) extended space G(T;X,Y,Z,S). In addition to Lorentz transformations (T;X),…
The Bloch sphere is a familiar and useful geometrical picture of the dynamics of a single spin or two-level system's quantum evolution. The analogous geometrical picture for three-level systems is presented, with several applications. The…
The Randall-Sundrum model is studied in 6 dimension with AdS$_4$ or dS$_4$ metric in the physical 4 dimensional space. Two solutions are found, one with induced 5-dimensional gravity terms added to the induced cosmological constant terms.…
We discuss the nature of the low-frequency quadrupole vibrations from small-amplitude to large-amplitude regimes. We consider full five-dimensional quadrupole dynamics including three-dimensional rotations restoring the broken symmetries as…
The conformal compactification is considered in a hierarchy of hypercomplex projective spaces with relevance in physics including Minkowski and Anti-de Sitter space. The geometries are expressed in terms of bicomplex Vahlen matrices and…
The cosmology in the Hubble expansion era of the Horava-Witten M-theory compactified on a Calabi-Yau threefold is studied in the reduction to five-dimensions where the effects of the Calabi-Yau manifold are summarized by the volume modulus,…
The Bohr compactification is a well known construction for (topological) groups and semigroups. Recently, this notion has been investigated for arbitrary structures in \cite{har_kun:bohr_discrete} where the Bohr compactification is defined,…
The supergroup OSp(8*|4), which is the superconformal group of (2,0) theory in six dimensions, is broken to the subgroup OSp(4|2)xOSp(4|2) by demanding the invariance of a certain product in a superspace with eight bosonic and four…
The coset spaces E$_8$/SO(10)$\times$H$_F$ allow complex structures which can account for three quark-lepton generations including right-handed neutrinos. We show that in the context of supersymmetric SO(10) gauge theories in 6 dimensions…
It is shown that self-dual theories generalize to four dimensions both the conformal and analytic aspects of two-dimensional conformal field theories. In the harmonic space language there appear several ways to extend complex analyticity…
For many classical moduli spaces of orthogonal type there are results about the Kodaira dimension. But nothing is known in the case of dimension greater than 19. In this paper we obtain the first results in this direction. In particular the…
We consider the cosmology of a ``3-brane universe'' in a five dimensional (bulk) space-time with a cosmological constant. We show that Einstein's equations admit a first integral, analogous to the first Friedmann equation, which governs the…
A classification of 2-dimensional surfaces imbedded in spacetime is presented, according to the algebraic properties of their shape tensor. The classification has five levels, and provides among other things a refinement of the concepts of…
We study symplectic embeddings of ellipsoids into balls. In the main construction, we show that a given embedding of 2m-dimensional ellipsoids can be suspended to embeddings of ellipsoids in any higher dimension. In dimension 6,s if the…
The Born-Infeld equation in two dimensions is generalised to higher dimensions whilst retaining Lorentz Invariance and complete integrability. This generalisation retains homogeneity in second derivatives of the field.
A $D$-dimensional Einstein-Gauss-Bonnet (EGB) flat cosmological model with a cosmological term $\Lambda$ is considered. We focus on solutions with exponential dependence of scale factor on time. Using previously developed general analysis…
A D-dimensional gravitational model with Gauss-Bonnet term is considered. When ansatz with diagonal cosmological type metrics is adopted, we find solutions with exponential dependence of scale factors (with respect to "synchronous-like"…
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…