commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

Let / be a real valued integrable function on a compact homogeneous space M = K\G and M¡ the operator of pointwise multiplication by /. The authors consider families of Toeplitz operators T¡P = PM¡P as P ranges over a net of orthogonal projections from L2(M) to finite dimensional G-invariant subspaces. Necessary and sufficient conditions are given on the net in order that the distribution of ei...

We introduce the notion of a semi-Riemannian spectral triple which generalizes the notion of spectral triple and allows for a treatment of semiRiemannian manifolds within a noncommutative setting. It turns out that the relevant spaces in noncommutative semi-Riemannian geometry are not Hilbert spaces any more but Krein spaces, and Dirac operators are Kreinselfadjoint. We show that the noncommuta...

A class of wormhole solutions is constructed that has restricted polar degrees freedom to achieve a gateway-like configuration. This compels the use distribution-valued metrics and connections which further neutrix product distributions, define curvature, Einstein tensor, other relevant quantities. The solution demands spacetime with non-Riemannian effects like non-metricity be consistent well-...

The Laplace-Beltrami operator of a smooth Riemannian manifold is determined by the Riemannian metric. Conversely, the heat kernel constructed from the eigenvalues and eigenfunctions of the Laplace-Beltrami operator determines the Riemannian metric. This work proves the analogy on Euclidean polyhedral surfaces (triangle meshes), that the discrete heat kernel and the discrete Riemannian metric (u...

1. Background. Intuitive arguments drawn from quantum mechanics and optics suggest that there should be some relation between the closed geodesies (periodic "particles") on a compact Riemannian manifold X and the eigenvalues (periodic "waves") of the Laplace-Beltrami operator A^. Indeed, in 1959, Huber [8] proved, for X a surface of constant negative curvature, that the set of lengths of closed...

Interval-valued intuitionistic fuzzy sets (IVIFSs) are widely used to handle uncertainty and imprecision in decision making. However, in more complicated environment, it is difficult to express the uncertain information by an IVIFS with considering the decision-making preference. Hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (G-GIVIFSS) which conta...