On a conformal manifold with boundary, we construct conformally invariant local boundary conditions B for the conformally invariant power of the Laplacian k , with the property that ( k , B) is formally self-adjoint. These boundary problems are used to construct conformally invariant nonlocal operators on the boundary Σ, generalizing the conformal Dirichlet-to-Robin operator, with principal par...

First and foremost, we show that a 4-dimensional conformally flat generalized Ricci recurrent spacetime $(GR)_4$ is an Einstein manifold. We examine such as solution of $f(R, G)$-gravity theory it shown the additional terms from modification gravitational sector can be expressed perfect fluid. Several energy conditions are investigated with G) = R +\sqrt{G}$ R^2+GlnG$. For both models, weak, nu...

Our goal in this paper is to obtain further information about the curvature of gradient shrinking Ricci solitons. This is important for a better understanding and ultimately for the classification of these manifolds. The classification of gradient shrinkers is known in dimensions 2 and 3, and assuming locally conformally flatness, in all dimensions n ≥ 4 (see [14, 13, 6, 15, 20, 12, 2]). Many o...

The null distance for Lorentzian manifolds was recently introduced by Sormani and Vega. Under mild assumptions on the time function of spacetime, gives rise to an intrinsic, conformally invariant metric that induces manifold topology. We show when warped products low regularity globally hyperbolic spacetimes endowed with are (local) integral current spaces. This structure sets stage investigati...