We obtain a characterization of the Kerr metric among stationary, asymptotically flat, vacuum spacetimes, which extends the characterization in terms of the Simon tensor (defined only in the manifold of trajectories) to the whole spacetime. More precisely, we define a three index tensor on any spacetime with a Killing field, which vanishes identically for Kerr and which coincides in the strictl...

We derive a class of variational functionals which arise naturally in conformal geometry. In the special case when the Riemannian manifold is locally conformal flat, the functional coincides with the well studied functional which is the integration over the manifold of the k-symmetric function of the Schouten tensor of the metric on the manifold.

Spacetimes have conventionally been described by a global Lorentzian metric on a differentiable four-manifold. Herein we explore the possibility of spacetimes defined by a connection, which is locally but not globally Levi-Civita. The general method of obtaining such connections is presented for the nondegenerate case followed by an example that modifies the Robertson-Walker spacetimes for flat...

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.

Abstract In this paper, we study locally projectively flat Finsler metrics of constant flag curvature. We find equations that characterize these by warped product. Using the obtained equations, manufacture new product vanishing These contain metric introduced Berwald and spherically symmetric given Mo-Zhu.

In this paper, we study locally strongly convex affine hypersurfaces with vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of metric. As main result, classify such being not flat particular, $2, 3$-dimensional are completely determined.

In this paper, a combination of algebraic and topological methods are applied to obtain new structural results on harmonic rings. Especially, it is shown that if Gelfand ring A modulo its Jacobson radical zero dimensional ring, then clean ring. It also proved that, for given A, the retraction map $${\text {Spec}}(A)\rightarrow {\text {Max}}(A)$$ flat continuous only Dually, mp-ring {Min}}(A)$$...

Exponential families and mixture families are parametric probability models that can be geometrically studied as smooth statistical manifolds with respect to any statistical divergence like the KullbackLeibler (KL) divergence or the Hellinger divergence. When equipping a statistical manifold with the KL divergence, the induced manifold structure is dually flat, and the KL divergence between dis...