We construct a Kähler structure (J,Ω, G) on the space L(H) of oriented geodesics of hyperbolic 3-space H and investigate its properties. We prove that (L(H), J) is biholomorphic to P×P−∆, where ∆ is the reflected diagonal, and that the Kähler metric G is of neutral signature, conformally flat and scalar flat. We establish that the identity component of the isometry group of the metric G on L(H)...

in this paper, we introduce a new class of implicit functions and also common property (e.a) in modified intuitionistic fuzzy metric spaces and utilize the same to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces besides discussing related results and illustrative examples. we are not aware of any paper dealing with such implicit functions in modified intuit...

we consider the concept of ω-distance on a complete partially ordered g-metric space and prove some common fi xed point theorems.

In [MW], Masur and Wolf proved that the Teichmüller space of genus g > 1 surfaces with the Teichmüller metric is not a Gromov hyperbolic space. In this paper, we provide an alternative proof based upon a study of the visual sphere of Teichmüller space.

We show that the open unit ball of the space of operators from a finite dimensional Hilbert space into a separable Hilbert space (we call it “operator ball”) has a restricted form of normal structure if we endow it with a hyperbolic metric (which is an analogue of

This is an article I wrote for Dynamics, Games, and Science. In Dynamics, Game, and Science, one of the most important equilibrium states is a Gibbs state. The deformation of a Gibbs state becomes an important subject in these areas. An appropriate metric on the space of underlying dynamical systems is going to be very helpful in the study of deformation. The Teichmüller metric becomes a natura...

For a Jordan domain in the plane the length metric space of points connected to an interior point by a curve of finite length is a cat(0) space and Gromov hyperbolic. With respect to the cone topology, that space plus its boundary at infinity is topologically the same as the original Jordan domain.

In this paper we introduce a hyperbolic (Poincaré-Bergman type) distance δ on the noncommutative open ball [B(H)]1 := n (X1, . . . ,Xn) ∈ B(H) n : ‖X1X ∗ 1 + · · ·+XnX ∗ n‖ 1/2 < 1 o , where B(H) is the algebra of all bounded linear operators on a Hilbert space H. It is proved that δ is invariant under the action of the free holomorphic automorphism group of [B(H)]1, i.e., δ(Ψ(X),Ψ(Y )) = δ(X, ...

In this paper, we show that the analogue of Thurston's asymmetric metric on Teichmüller space flat structures torus is weak Finsler and give a geometric description its unit circle at each point in tangent to space. We then introduce family metrics which interpolate between (which coincides with hyperbolic metric). describe circles family.