In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth order Riemann-Lovelock tensor is determined by its traces in dimensions 2k ≤ D < 4k. In...

We consider a complex Hermitian manifold of complex dimensions four with a Hermitian metric and a Chern connection. It is shown that the action that determines the dynamics of the metric is unique, provided that the linearized Einstein action coupled to an antisymmetric tensor is obtained, in the limit when the imaginary coordinates vanish. The unique action is of the Chern-Simons type when exp...

A wavelike scalar-Einstein solution is found and indicating vectors constructed from the Bel-Robinson tensor are used to study which objects co-move with wave whether gravitational energy transfer null. It that this criteria gives null for both vacuum plane scalar wave.

According to a classical result of E. Calabi any hyperbolic affine hypersphere endowed with its natural Hessian metric has a non-positive Ricci tensor. The affine hyperspheres can be described as the level sets of solutions to the “hyperbolic” toric Kähler-Einstein equation e = detDΦ on proper convex cones. We prove a generalization of this theorem showing that for every Φ solving this equation...

We construct a Lagrangian of Weyl spinors and gauge fields, which is invariant under the action of equivalent local transformations on the spinor algebra representations. A model of vacuum with a nontrivial gauge strength-tensor setting a scale is suggested, so that the leading approximation at low energies is described by the Einstein–Hilbert Lagrangian of gravity. We consider a mechanism for ...

A relativistic modified gravity (MOG) called Scalar-Tensor-Vector Gravity (STVG) desribes a self-consistent, stable gravity theory that contains Einstein’s general relativity in a well-defined limit. The theory has an extra degree of freedom, a vector field called a “phion” field whose curl is a skew symmetric field that couples to matter (“fifth force”). The spacetime geometry is described by ...

Classical general relativity from quantum gravity and the generalized Kodama states. Abstract In this paper we investigate the relation between the CDJ matrix used for construction of the generalized Kodama states and the Weyl curvature tensor. By exploiting special self-duality relations unique to four dimensional spacetime, we show that the effects of quantum gravity in Ashtekar variables are...

The aim of this paper is to extend the notion all known quasi-Einstein manifolds like generalized quasi-Einstein, mixed manifold, pseudo manifold and many more name it comprehensive quasi Einstein C(QE)$_{n}$. We investigate some geometric physical properties C(QE)$_{n}$ under certain conditions. study conformal conharmonic mappings between manifolds. Then we examine with harmonic Weyl tensor. ...

In this work, we study the inflationary cosmology in modified gravity theory [Formula: see text] ([Formula: is parameter) with three distinct classes of inflation potentials (i) text], (ii) and (iii) where are potential parameters. We have derived Einstein equation, slow-roll parameters, scalar spectral index tensor-to-scalar ratio r tensor theory. obtain range using constraints parameter space...

We provide a sufficient condition for the local stability of closed Einstein manifolds positive Ricci curvature under iteration in terms spectrum Lichnerowicz Laplacian acting on divergence-free tensor fields. use this result to consider several iteration, including symmetric spaces compact type.