Related papers: On pseudo-Hermitian Einstein spaces

We introduce a generalisation of Fefferman's conformal circle bundle over a contact Cauchy-Riemann three-manifold. These can be viewed as exact `perturbations' of Fefferman's structure by a semi-basic one-form, which encodes additional data…

The conventional quantum geometric tensor (QGT) is Hermitian, with a real symmetric quantum metric and an imaginary antisymmetric Berry curvature. We show that the Zeeman QGT is generically non-Hermitian and admits a natural decomposition…

Many important features of a field theory, {\it e.g.}, conserved currents, symplectic structures, energy-momentum tensors, {\it etc.}, arise as tensors locally constructed from the fields and their derivatives. Such tensors are naturally…

We prove that there are infinitely many pairs of homeomorphic non-diffeomorphic smooth 4-manifolds, such that in each pair one manifold admits an Einstein metric and the other does not. We also show that there are closed 4-manifolds with…

We extend the basic formalism of mimetic-metric-torsion gravity theory, in a way that the mimetic scalar field can manifest itself geometrically as the source of not only the trace mode of torsion, but also its axial (or, pseudo-trace)…

In this note we give a characterization of Kaehler metrics which are both Calabi extremal and Kaehler-Ricci solitons in terms of complex Hessians and the Riemann curvature tensor. We apply it to prove that, under the assumption of…

A general formula is calculated for the connection of a central metric w.r.t.\ a noncommutative spacetime of Lie-algebraic type. This is done by using the framework of linear connections on central bi-modules. The general formula is further…

In this article we give general neccessary and sufficient conditions to ensure that a pseudo-Riemannian manifold is conformal to an Einstein space. These conditions are algorithmic in \emph{the metric tensor} whenever the Weyl endomorphism…

We answer in the affirmative the question posed by Conti and Rossi on the existence of nilpotent Lie algebras of dimension 7 with an Einstein pseudo-metric of nonzero scalar curvature. Indeed, we construct a left-invariant pseudo-Riemannian…

The formalism for non-Hermitian quantum systems sometimes blurs the underlying physics. We present a systematic study of the vielbein-like formalism which transforms the Hilbert space bundles of non-Hermitian systems into the conventional…

In the context of mathematical cosmology, the study of necessary and sufficient conditions for a semi-Riemannian manifold to be a (generalised) Robertson-Walker space-time is important. In particular, it is a requirement for the development…

When real Lorentzian spacetime is embedded into a manifold parametrized by higher division algebras (complex or quaternion with Hermitean metric) and the representation constraints of their symmetry groups are made compatible, a set of…

We classify weakly Einstein algebraic curvature tensors in an oriented Euclidean 4-space, defined by requiring that the three-index contraction of the curvature tensor against itself be a multiple of the inner product. This algebraic…

We derive the general formulas for a special configuration of the sequential warped product semi-Riemannian manifold to be Einstein, where the base-manifold is the product of two manifolds both equipped with a conformal metrics.…

We prove that $T^2$-invariant Einstein metrics with non-negative sectional curvature on a four-manifold are locally symmetric.

In this article, we achieved several non-naturally reductive Einstein metrics on exceptional simple Lie groups, which are formed by the decomposition arising from general Wallach spaces. By using the decomposition corresponding to the two…

The Wasserstein distance on multivariate non-degenerate Gaussian densities is a Riemannian distance. After reviewing the properties of the distance and the metric geodesic, we present an explicit form of the Riemannian metrics on…

In the conventional Schr\"{o}dinger's formulation of quantum mechanics the unitary evolution of a state $\psi$ is controlled, in Hilbert space ${\cal L}$, by a Hamiltonian $\mathfrak{h}$ which must be self-adjoint. In the recent,…

In this brief article an internal symmetry of a generic metric compatible space-time connection, metric and generalized volume element is introduced. The symmetry arises naturally by considering a space-time connection containing a generic…

In this paper, we study a class of Finsler metrics called general (\alpha,\beta)-metrics, which are defined by a Riemannian metric and an 1-form. We construct some general (\alpha,\beta)-metrics with constant Ricci curvature.