Related papers: Geometry and Physics on $w_{\infty}$ Orbits
Consider the cyclic group C_2 of order two acting by complex-conjugation on the unit circle S^1. The main result is that a finitely dominated manifold W of dimension > 4 admits a cocompact, free, discontinuous action by the infinite…
We present a revisitation of the Almheiri-Polchinski dilaton gravity model from a two-dimensional (2D) bulk perspective. We describe a peculiar feature of the model, namely the pattern of conformal symmetry breaking using bulk Killing…
It is shown that the reduced particle dynamics of 2+1 dimensional gravity in the maximally slicing gauge is of hamiltonian nature. We give the exact diffeomorphism which transforms the expression of the spinning cone geometry in the Deser,…
This paper meticulously revisit and study the flux geometry of any compact oriented manifold $(M; W)$. We generalize several well-known factorization results, exhibit some orbital conditions for the study of flux geometry, give a proof of…
In this paper, we study the holography of quasi-topological gravity in several aspects. We redo the calculation of shear viscosity on the boundary CFT with a new method which is associated with conserved Noether current and show that it has…
The hodograph of the Kepler-Coulomb problem, that is, the path traced by its velocity vector, is shown to be a circle and then it is used to investigate other properties of the motion. We obtain the configuration space orbits of the problem…
The Lie-Poisson algebra so(N+1) and some of its contractions are used to construct a family of superintegrable Hamiltonians on the ND spherical, Euclidean, hyperbolic, Minkowskian and (anti-)de Sitter spaces. We firstly present a…
We formulate the uniformisation problem underlying the geometry of W_n-gravity using the differential equation approach to W-algebras. We construct W_n-space (analogous to superspace in supersymmetry) as an (n-1) dimensional complex…
First, I construct an isomorphism between the categories of (topological) groups of nilpotency class 2 with 2-divisible center and (topological) Lie rings of nilpotency class 2 with 2-divisible center. That isomorphism allows us to…
We study the rigidity of compact submanifolds of Riemannian manifolds of arbitrary codimension that satisfy a sharp pinching condition involving the norm of the second fundamental form and the mean curvature. Without assuming that the…
We show that W_3 is the algebra of symmetries of the ``rigid-particle'', whose action is given by the integrated extrinsic curvature of its world line. This is easily achived by showing that its equation of motion can be written in terms of…
We describe a class of coadjoint orbits of the group of Hamiltonian diffeomorphisms of a symplectic manifold $(M,\omega)$ by implementing symplectic reduction for the dual pair associated to the Hamiltonian description of ideal fluids. The…
This dissertation represents work on three different subjects relating to quantum gravity and the AdS/CFT correspondence. First, we review a holographic computation of the one-loop corrections to the Weyl anomaly on Ricci flat backgrounds…
We investigate the occurrence of divergences in maximal supergravity in various dimensions from the point of view of supersymmetry constraints on the U-duality invariant threshold functions defining the higher derivative couplings in the…
The integrability of $R^2$-gravity with torsion in two dimensions is traced to an ultralocal dynamical symmetry of constraints and momenta in Hamiltonian phase space. It may be interpreted as a quadratically deformed $iso(2,1)$-algebra with…
The mechanics of an oriented point (point with "spin") based on 3D and 4D Frenet equations is considered. In such mechanics there is an opportunity to describe formally any physical trajectory of a particle with own rotation. We use…
The constraint structure of 2D-gravity with the Weyl and area-preserving diffeomorphism invariances is analysed in the ADM formulation. It is found that when the area-preserving diffeomorphism constraints are kept, the usual conformal gauge…
We work on a 4-manifold equipped with Lorentzian metric $g$ and consider a volume-preserving diffeomorphism which is the unknown quantity of our mathematical model. The diffeomorphism defines a second Lorentzian metric $h$, the pullback of…
Let $f:M\to M$ be a $C^{1+\epsilon}$-map on a smooth Riemannian manifold $M$ and let $\Lambda\subset M$ be a compact $f$-invariant locally maximal set. In this paper we obtain several results concerning the distribution of the periodic…
The massive non-relativistic free particle in d-1 space dimensions has an action with a surprizing non-linearly realized SO(d,2) symmetry. This is the simplest example of a host of diverse one-time-physics systems with hidden SO(d,2)…