This article gives an up-to-date account of the theory of discrete group actions on non-Riemannian homogeneous spaces. As an introduction of the motifs of this article, we begin by reviewing the current knowledge of possible global forms of pseudoRiemannian manifolds with constant curvatures, and discuss what kind of problems we propose to pursue. For pseudo-Riemannian manifolds, isometric acti...

This article gives an up-to-date account of the theory of discrete group actions on non-Riemannian homogeneous spaces. As an introduction of the motifs of this article, we begin by reviewing the current knowledge of possible global forms of pseudoRiemannian manifolds with constant curvatures, and discuss what kind of problems we propose to pursue. For pseudo-Riemannian manifolds, isometric acti...

Integrability of the Wess–Zumino–Witten model as a non–ultralocal theory * Abstract We consider the 2–dimensional Wess–Zumino–Witten (WZW) model in the canon-ical formalism introduced in [5]. Using an r–s matrix approach to non–ultralocal field theories we find the Poisson algebra of monodromy matrices and of conserved quantities with a new, non–

An example is given of a plane topological torsion defect representing a cosmic wall double wall in teleparallel gravity.The parallel planar walls undergone a repulsive gravitational force due to Cartan torsion.This is the first example of a non-Riemannian double cosmic wall.It is shown that the walls oscillate with a speed that depends on torsion and on the surface density of the wall.Cartan t...

Let M be a compact Riemannian manifold and h a smooth function on M. Let h (x) = inf jvj=1 (Ric x (v; v) ? 2Hess(h) x (v; v)). Here Ric x denotes the Ricci curvature at x and Hess(h) is the Hessian of h. Then M has nite fundamental group if h ? h < 0. Here h =: + 2L rh is the Bismut-Witten Laplacian. This leads to a quick proof of recent results on extension of Myers' theorem to mani-folds with...

We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...

The existence of the Laplace-Beltrami operator has allowed mathematicians to carry out Fourier analysis on Riemannian manifolds [2]. We recall that the Laplace-Beltrami operator ∆ on a compact Riemannian manifold has a discrete set of eigenvalues {λj}j=1, which satisfies λj →∞ as j →∞. This is known as the spectrum of the Laplace-Beltrami operator. Inverse spectral geometry studies how much of ...

Let (V, g) and (W,h) be compact Riemannian manifolds of dimension at least 3. We derive a lower bound for the conformal Yamabe constant of the product manifold (V × W, g + h) in terms of the conformal Yamabe constants of (V, g) and (W,h).

Using Seiberg-Witten theory, it is shown that any Kähler metric of constant negative scalar curvature on a compact 4-manifold M minimizes the L-norm of scalar curvature among Riemannian metrics compatible with a fixed decomposition H(M) = H ⊕ H−. This implies, for example, that any such metric on a minimal ruled surface must be locally symmetric.

Analyzing shape manifolds as Riemannian manifolds has been shown to be an effective technique for understanding their geometry. Riemannian metrics of the type H and H on the space of planar curves have already been investigated in detail. Since in many applications, the basic shape of an object is understood to be independent of its scale, orientation or placement, we consider here an H metric ...