Search results for "metric space."

Poisson Geometry in Mathematics and Physics

2008

We realize quantized anti de Sitter space black holes, building Connes spectral triples, similar to those used for quantized spheres but based on Universal Deformation Quantization Formulas (UDF) obtained from an oscillatory integral kernel on an appropriate symplectic symmetric space. More precisely we first obtain a UDF for Lie subgroups acting on a symplectic symmetric space M in a locally simply transitive manner. Then, observing that a curvature contraction canonically relates anti de Sitter geometry to the geometry of symplectic symmetric spaces, we use that UDF to define what we call Dirac-isospectral noncommutative deformations of the spectral triples of locally anti de Sitter black…

A fixed point theorem for G-monotone multivalued mapping with application to nonlinear integral equations

2017

We extend notion and theorem of [21] to the case of a multivalued mapping defined on a metric space endowed with a finite number of graphs. We also construct an example to show the generality of our result over existing results. Finally, we give an application to nonlinear integral equations

On generalized weakly G-contraction mapping in G-metric spaces

2011

AbstractIn this paper, we establish some common fixed point results for two self-mappings f and g on a generalized metric space X. To prove our results we assume that f is a generalized weakly G-contraction mapping of types A and B with respect to g.

Quasihyperbolic boundary condition: Compactness of the inner boundary

2011

We prove that if a metric space satisfies a suitable growth condition in the quasihyperbolic metric and the Gehring–Hayman theorem in the original metric, then the inner boundary of the space is homeomorphic to the Gromov boundary. Thus, the inner boundary is compact. peerReviewed

Metric Lie groups admitting dilations

2019

We consider left-invariant distances $d$ on a Lie group $G$ with the property that there exists a multiplicative one-parameter group of Lie automorphisms $(0, \infty)\rightarrow\mathtt{Aut}(G)$, $\lambda\mapsto\delta_\lambda$, so that $ d(\delta_\lambda x,\delta_\lambda y) = \lambda d(x,y)$, for all $x,y\in G$ and all $\lambda>0$. First, we show that all such distances are admissible, that is, they induce the manifold topology. Second, we characterize multiplicative one-parameter groups of Lie automorphisms that are dilations for some left-invariant distance in terms of algebraic properties of their infinitesimal generator. Third, we show that an admissible left-invariant distance on a Lie …

Geodesics on spaces of almost hermitian structures

1994

A natural metric on the space of all almost hermitian structures on a given manifold is investigated.

Hermitian natural differential operators

1986

Wormholes and nonsingular spacetimes in Palatinif(R)gravity

2015

We reconsider the problem of $f(R)$ theories of gravity coupled to Born-Infeld theory of electrodynamics formulated in a Palatini approach, where metric and connection are independent fields. By studying electrovacuum configurations in a static and spherically symmetric space-time, we find solutions which reduce to their Reissner-Nordstr\"om counterparts at large distances but undergo important non-perturbative modifications close to the center. Our new analysis reveals that the point-like singularity is replaced by a finite-size wormhole structure, which provides a geodesically complete and thus nonsingular space-time, despite the existence of curvature divergences at the wormhole throat. …

Flat synchronizations in spherically symmetric space-times

2010

It is well known that the Schwarzschild space-time admits a spacelike slicing by flat instants and that the metric is regular at the horizon in the associated adapted coordinates (Painleve-Gullstrand metric form). We consider this type of flat slicings in an arbitrary spherically symmetric space-time. The condition ensuring its existence is analyzed, and then, we prove that, for any spherically symmetric flat slicing, the densities of the Weinberg momenta vanish. Finally, we deduce the Schwarzschild solution in the extended Painleve-Gullstrand-Lemaitre metric form by considering the coordinate decomposition of the vacuum Einstein equations with respect to a flat spacelike slicing.

Generalized countable iterated function systems

2011

One of the most common and most general way to generate fractals is by using iterated function systems which consists of a finite or infinitely many maps. Generalized countable iterated function systems (GCIFS) are a generalization of countable iterated function systems by considering contractions from X ? X into X instead of contractions on the metric space X to itself, where (X, d) is a compact metric space. If all contractions of a GCIFS are Lipschitz with respect to a parameter and the supremum of the Lipschitz constants is finite, then the associated attractor depends continuously on the respective parameter.