We study a novel class of nonsingular time-symmetric cosmological bounces. In this class of four dimensional models the bounce is induced by a perfect fluid with a negative energy density. Metric perturbations are solved in an analytic way all through the bounce. The conditions for generating a scale invariant spectrum of tensor and scalar metric perturbations are discussed.

A Riemann-Lie algebra is a Lie algebra G such that its dual G∗ carries a Riemannian metric compatible (in the sense introduced by the author in C. R. Acad. Sci. Paris, t. 333, Série I, (2001) 763–768) with the canonical linear Poisson structure of G∗ . The notion of Riemann-Lie algebra has its origins in the study, by the author, of Riemann-Poisson manifolds (see Differential Geometry and its A...

The global holomorphic invariant αG(M) introduced by Tian[14], Tian and Yau[13] is closely related to the existence of Kähler-Einstein metrics. In his solution to the Calabi conjecture, Yau[19] proved the existence of a Kähler-Einstein metric on compact Kähler manifolds with nonpositive first Chern class. Kähler-Einstein metrics do not always exist in the case when the first Chern class is posi...

We show that if a locally compact group G acts properly on a locally compact σ-compact space X, then there is a family of G-invariant proper continuous finite-valued pseudometrics which induces the topology of X. If X is, furthermore, metrizable, then G acts properly on X if and only if there exists a G-invariant proper compatible metric on X.

The paper generalises Thompson and Hilbert metric to the space of spectral densities. The resulting complete metric space has the differentiable structure of a Finsler manifold with explicit geodesics. Additionally, in the rational case, the resulting distance is filtering invariant and can be computed efficiently.

We derive the (g − 2)(g − 3)/2 linearly independent relations among the products of pairs in a basis of holomorphic abelian differentials in the case of compact non-hyperelliptic Riemann surfaces of genus g ≥ 4. By the Kodaira-Spencer map this leads to the modular invariant metric on the moduli space induced by the Siegel metric.

The evolution of the inflaton field fluctuations from gauge-invariant metric fluctuations is discussed. In particular, the case of a symmetric φ c-exponential potential is analyzed.

Strengthening a theorem of Hjorth this paper gives a new characterization of which Polish groups admit compatible complete left invariant metrics. As a corollary it is proved that any Polish group without a complete left invariant metric has a continuous action on a Polish space whose associated orbit equivalence relation is not essentially countable.