In this paper, we compute Riemannian metrics on the Siegel-Jacobi space which are invariant under the natural action of the Jacobi group explicitly and also provide the Laplacians of these invariant metrics. These are expressed in terms of the trace form.

In this paper, we compute Riemannian metrics on the Siegel-Jacobi space which are invariant under the natural action of the Jacobi group explicitly and also provide the Laplacians of these invariant metrics. These are expressed in terms of the trace form.

In this paper, we compute Riemannian metrics on the Siegel-Jacobi space which are invariant under the natural action of the Jacobi group explicitly and also provide the Laplacians of these invariant metrics. These are expressed in terms of the trace form.

We nd a Gaussian oo-diagonal heat kernel estimate for uniformly elliptic operators with measurable coeecients acting on regions R N , where the order 2m of the operator satisses N < 2m. The estimate is expressed using certain Riemannian-type metrics, and a geometrical result is established allowing conversion of the estimate into terms of the usual Riemannian metric on. Work of Barbatis 1] is a...

We show that the Riemannian Kerr solutions are the only Riemannian, Ricci-flat and asymptotically flat C2-metrics gμν on a 4dimensional complete manifold M of topology R2×S2 which have (at least) a 1-parameter group of periodic isometries with only isolated fixed points (”nuts”) and with orbits of bounded length at infinity. ∗Present address: Institut für theoretische Physik der Univ. Wien, Bol...

We construct the moduli space of r−jets of Riemannian metrics at a point on a smooth manifold. The construction is closely related to the problem of classification of jet metrics via differential invariants. The moduli space is proved to be a differentiable space which admits a finite canonical stratification into smooth manifolds. A complete study on the stratifica-tion of moduli spaces is car...

We investigate connections between pairs of Riemannian metrics whose sum is a (tensor) product of a covector field with itself. As a special result is constructed one-to-one mapping between the classes of Euclidean and Lorentzian metrics. The existence of Lorentzian metrics on a differentiable manifold is discussed. We point the possibility that any physical theory based on Lorentzian metric(s)...

In this paper, we define a new projective invariant and call it W̃ -curvature. We prove that a Finsler manifold with dimension n ≥ 3 is of constant flag curvature if and only if its W̃ -curvature vanishes. Various kinds of projectively flatness of Finsler metrics and their equivalency on Riemannian metrics are also studied. M.S.C. 2010: 53B40, 53C60.

Let Dn be the generalized unit disk of degree n. In this paper, we compute Riemannian metrics on Dn × C (m,n) which are invariant under the natural action of the Jacobi group explicitly and also provide the Laplacians of these invariant metrics. These are expressed in terms of the trace form.

A method, due tó Elie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2,2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is s...