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We review the geometrical properties of vacuum spacetimes in (2+1)-gravity with vanishing cosmological constant. We explain how these spacetimes are characterised as quotients of their universal cover...
A universe much like the (Euclidean) de Sitter space-time appears as background geometry in the causal dynamical triangulation (CDT) regularization of quantum gravity. We study the geometry of such un...
We derive a transformation of the noncommutative geometry inspired Schwarzschild solution into new coordinates such that the apparent unphysical singularities of the metric are removed. Moreover, we...
We discuss the use of information geometry in black hole physics and present the outcomes. The type of information geometry we utilize in this approach is the thermodynamic (Ruppeiner) geometry define...
We consider an observer in a (2+1)-spacetime without matter and cosmological constant who measures spacetime geometry by emitting lightrays which return to him at a later time. We investigate several ...
We show how an observer could measure the non-local holonomy variables that parametrise the flat Lorentzian 3d manifolds arising as spacetimes in (2+1)-gravity. We consider an observer who emits light...
"Acoustic spacetimes", in which techniques of differential geometry are used to investigate sound propagation in moving fluids, have attracted considerable attention over the last few decades. Most o...
Kerr-Schild (KS) geometry is based on a congruence of twistor null lines which forms a holographic space-time determined by the Kerr theorem. We describe in details integration of the non-stationary D...
The moduli spaceMg,k of Riemann surfaces of genus g with k punctures plays an important role in many area of mathematics and theoretical physics.In this article we first survey some of our recent work...
In a previous article we defined ”combined manifold” M3 as the graph of a diffeomorphism from one manifold M1 to another M2, akin to the idea of a diagonal map. In this paper, we derive the values for...
The effects of ultrasound on the dynamics of an air-water meniscus in a planar micro-geometry are investigated experimentally. The sonicated meniscus exhibits harmonic traveling waves or standing wave...
This article is a local analysis of integrable GL(2)-structures of degree 4. A GL(2)-structure of degree n corresponds to a distribution of rational normal cones over a manifold M of dimension (n+1). ...
Extensive studies of Norwegian rock-slope failure areas support a subdivision into three principle types: (1) Rockfall areas, (2) rockslide areas, and (3) complex fields. The classification is based o...
A gravitational collapse structure, 155 km long with a maximum width of 35 km, has been released as a single slope failure in the Storegga region off western Norway. The released volume of sediment, w...
With dynamic mediums such as computer displays, we propose a new kind of visually dynamic presentation of proofs in plane geometry. In asingle diagram for the proof, when the proof text goes on step b...

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