We discuss D-dimensional scalar field interacting with a scale invariant random metric which is either a Gaussian field or a square of a Gaussian field. The metric depends on d dimensional coordinates (where d < D). By a projection to a lower dimensional subspace we obtain a scale invariant non-Gaussian model of Euclidean quantum field theory in D − d or d dimensions.

We obtain analytic solutions for the density contrast and the anisotropic pressure in a multi-dimensional FRW cosmology with collisionless, massless matter. These are compared with perturbations of a perfect fluid universe. To describe the metric perturbations we use manifest gauge invariant metric potentials. The matter perturbations are calculated by means of (automatically gauge invariant) f...

We investigate consequences of allowing the Hilbert space of a quantum system to have a time-dependent metric. For a given possibly nonstationary quantum system, we show that the requirement of having a unitary Schrödinger time-evolution identifies the metric with a positive-definite (Ermakov-Lewis) dynamical invariant of the system. Therefore the geometric phases are determined by the metric. ...

Conformal invariant new forms of p-brane and Dp-brane actions are proposed. These are quadratic in ∂X for the p-brane case and for Dp-branes in the Abelian field strength. The fields content of these actions are: an induced metric, gauge fields, an auxiliary metric and an auxiliary scalar field. The proposed actions are Weyl invariant in any dimension and the elimination of the auxiliary metric...

In the present paper a global conformal invariant Y of a closed initial data set is constructed. A spacelike hypersurface Σ in a Lorentzian spacetime naturally inherits from the spacetime metric a differentiation De, the so-called real Sen connection, which turns out to be determined completely by the initial data hab and χab induced on Σ, and coincides, in the case of vanishing second fundamen...

In this article we consider the possible sets of distances in Polish metric spaces. By a Polish metric space we mean a pair (X, d), where X is a Polish space (a separable, completely-metrizable space) and d is a complete, compatible metric for X. We will consider two aspects. First, we will characterize which sets of reals can be the set of distances in a Polish metric space. We will also obtai...

This paper focuses on the study of open curves in a manifold M , and proposes a reparameterization invariant metric on the space of such paths. We use the square root velocity function (SRVF) introduced by Srivastava et al. in [11] to define a reparameterization invariant metric on the space of immersions M = Imm([0,1], M) by pullback of a metric on the tangent bundle TM derived from the Sasaki...

The object of this paper is to study invariant submanifolds M of Kenmotsu manifolds M̃ admitting a quarter symmetric metric connection and to show that M admits quarter symmetric metric connection. Further it is proved that the second fundamental forms σ and σ with respect to LeviCivita connection and quarter symmetric metric connection coincide. Also it is shown that if the second fundamental f...

We study three Möbius invariant metrics, and three affine invariant analogs, all of which are bilipschitz equivalent to the Poincaré hyperbolic metric. We exhibit numerous illustrative examples.