Our main goal in this paper is to construct the first explicit fundamental domain of the Picard modular group acting on the complex hyperbolic space CH . The complex hyperbolic space is a Hermitian symmetric space, its bounded realization is the unit ball in C equipped with the Bergman metric. The Picard modular group is a discontinuous holomorphic automorphism subgroup of SU(2, 1) with Gaussia...

we obtain two fixed point theorems for a kind of $varphi $-contractions incomplete fuzzy metric spaces, which are applied to easily deduceintuitionistic versions that improve and simplify the recent results of x.huang, c. zhu and x. wen.

in this paper,  the concept of fuzzy metric-like spaces is introduced which generalizes  the notion of fuzzy metric spaces given by george and veeramani cite{vee1}. some fixed point results for fuzzy contractive mappings on fuzzy metric-like spaces are derived. these results generalize several comparable results from the current literature. we also provide illustrative examples in support of ou...

Every point in Teichmüller space is a hyperbolic metric on a given Riemann surface, therefore, a Weil-Petersson geodesic in Teichmüller space can be viewed as a 3-manifold. We investigate the sectional curvatures of this 3-manifold, with a natural metric. We obtain explicit formulas for the curvature tensors of this metric, and show that the “average”s of them are zero, and hence the geometry o...

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a metric space. Further properties of this metric space are studied in the next papers. The importance of the work can be situated in fields such as cosmology, quan...

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance which makes this moduli space into a metric space. Further properties of this metric space are studied in the next papers. The importance of the work can be situated in fields such as cosmology, quan...

We prove Liouville theorems for Dirac-harmonic maps from the Euclidean space Rn, the hyperbolic space Hn and a Riemannian manifold Sn (n ≥ 3) with the Schwarzschild metric to any Riemannian manifold N .

We study the information metric on instanton moduli spaces in two-dimensional nonlinear σ models. In the CP 1 model, the information metric on the moduli space of one instanton with the topological charge Q = k (k ≥ 1) is a three-dimensional hyperbolic metric, which corresponds to Euclidean anti–de Sitter space-time metric in three dimensions, and the overall scale factor of the information met...

We study the information metric on instanton moduli spaces in two-dimensional nonlinear sigma models. In the CP1 model, the information metric on the moduli space of one instanton with the topological charge Q=k(k > or =1) is a three-dimensional hyperbolic metric, which corresponds to Euclidean anti-de Sitter space-time metric in three dimensions, and the overall scale factor of the information...