Kaluza-Klein dimensional reduction and Gauss-Codazzi-Ricci equations

In this paper we imitate the traditional method which is used customarily in the General Relativity and some mathematical literatures to derive the Gauss-Codazzi-Ricci equations for dimensional reduction. It would be more distinct concerning geometric meaning than the vielbein method. Especially, if the lower dimensional metric is independent of reduced dimensions the counterpart of the symmetric extrinsic curvature is proportional to the antisymmetric Kaluza-Klein gauge field strength. For isometry group of internal space, the SO(n) symmetry and SU(n) symmetry are discussed. And the Kaluza-Klein instanton is also enquired.Comment: 15 page

The relation between the two-point and the three-point correlation functions in the non-linear gravitational clustering regime

The connection between the two-point and the three-point correlation functions in the non-linear gravitational clustering regime is studied. Under a scaling hypothesis, we find that the three-point correlation function, $\zeta$, obeys the scaling law $\zeta\propto \xi^{\frac{3m+4w-2\epsilon}{2m+2w}}$ in the nonlinear regime, where $\xi$, $m$, $w$, and $\epsilon$ are the two-point correlation function, the power index of the power spectrum in the nonlinear regime, the number of spatial dimensions, and the power index of the phase correlations, respectively. The new formula reveals the origin of the power index of the three-point correlation function. We also obtain the theoretical condition for which the ``hierarchical form'' $\zeta\propto\xi^2$ is reproduced.Comment: 16 pages, 4 figures. Accepted for publication in APJ. Some sentences and figures are revise

Toric moment mappings and Riemannian structures

Coadjoint orbits for the group SO(6) parametrize Riemannian G-reductions in six dimensions, and we use this correspondence to interpret symplectic fibrations between these orbits, and to analyse moment polytopes associated to the standard Hamiltonian torus action on the coadjoint orbits. The theory is then applied to describe so-called intrinsic torsion varieties of Riemannian structures on the Iwasawa manifold.Comment: 25 pages, 14 figures; Geometriae Dedicata 2012, Toric moment mappings and Riemannian structures, available at http://www.springerlink.com/content/yn86k22mv18p8ku2

N=2 Boundary conditions for non-linear sigma models and Landau-Ginzburg models

We study N=2 nonlinear two dimensional sigma models with boundaries and their massive generalizations (the Landau-Ginzburg models). These models are defined over either Kahler or bihermitian target space manifolds. We determine the most general local N=2 superconformal boundary conditions (D-branes) for these sigma models. In the Kahler case we reproduce the known results in a systematic fashion including interesting results concerning the coisotropic A-type branes. We further analyse the N=2 superconformal boundary conditions for sigma models defined over a bihermitian manifold with torsion. We interpret the boundary conditions in terms of different types of submanifolds of the target space. We point out how the open sigma models correspond to new types of target space geometry. For the massive Landau-Ginzburg models (both Kahler and bihermitian) we discuss an important class of supersymmetric boundary conditions which admits a nice geometrical interpretation.Comment: 48 pages, latex, references and minor comments added, the version to appear in JHE

On the Cartan Model of the Canonical Vector Bundles over Grassmannians

We give a representation of canonical vector bundles over Grassmannian manifolds as non-compact affine symmetric spaces as well as their Cartan model in the group of the Euclidean motions.Comment: 6 page