Anti-de Sitter space, squashed and stretched

Anti De Sitter Space, Squashed and Stretched

We study the Lorentzian analogues of the squashed 3-sphere, namely 2+1 dimensional anti-de Sitter space squashed or stretched along fibres that are either spacelike or timelike. The causal structure, and the property of being an Einstein–Weyl space, depend critically on whether we squash or stretch. We argue that squashing, and stretching, completely destroys the conformal boundary of the unsqu...

Super algebra and Harmonic Oscillator in Anti de Sitter space

The harmonic oscillator in anti de Sitter space(AdS) is discussed. We consider the harmonic oscillator potential and then time independent Schrodinger equation in AdS space. Then we apply the supersymmetric Quantum Mechanics approach to solve our differential equation. In this paper we have solved Schrodinger equation for harmonic oscillator in AdS spacetime by supersymmetry approach. The shape...

‎Spacelike hypersurfaces with constant $S$ or $K$ in de Sitter‎ ‎space or anti-de Sitter space

‎Let $M^n$ be an $n(ngeq 3)$-dimensional complete connected and‎ ‎oriented spacelike hypersurface in a de Sitter space or an anti-de‎ ‎Sitter space‎, ‎$S$ and $K$ be the squared norm of the second‎ ‎fundamental form and Gauss-Kronecker curvature of $M^n$‎. ‎If $S$ or‎ ‎$K$ is constant‎, ‎nonzero and $M^n$ has two distinct principal‎ ‎curvatures one of which is simple‎, ‎we obtain some‎ ‎charact...

Cohomogeneity One Anti De Sitter Space H_1^3

Gödel metric as a squashed anti–de Sitter geometry

We show that the non flat 2+1 dimensional factor of Gödel’s metric can be seen as belonging to a one parameter family of squashed anti–de Sitter geometries, with or without causal pathologies. We give a global algebraic isometric embedding of these metrics in 4+3 or 3+4 dimensional flat spaces, thereby illustrating the occurrence of the closed timelike curves. Mâıtre de Recherches F.N.R.S. E-ma...