Related papers: The Weyl Tensor of Gradient Ricci Solitons

[Dedicated to Richard S. Hamilton on forty years of Ricci flow] Gradient Ricci solitons have garnered significant attention both as self-similar solutions and singularity models of the Ricci flow. This survey article starts with a list of…

A Ricci soliton is a natural generalization of an Einstein metric. On a pseudo-Riemannian manifold (M, g), it is defined by : $LX g + \r{ho} = {\lambda} g, where X is a smooth vector field on M , LX denotes the Lie derivative in the…

We demonstrate the ``peeling property'' of the Weyl tensor in higher dimensions in the case of even dimensions (and with some additional assumptions), thereby providing a first step towards understanding of the general peeling behaviour of…

A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and…

The curvature of a higher spin potential as constructed in a previous article of the same authors arXiv:0705.3528 is applied to the analysis of the linearized trace anomaly obtained from the quadratic part of the effective action for a…

Within vacuum Weyl gravity, we obtain a solution by which, using different choices of the conformal factor, we derive metrics describing (i)~a bounce of the universe; (ii)~toroidal and spherical wormholes; and (iii)~a change in metric…

We derive point-wise and integral rigidity/gap results for a closed manifold with harmonic Weyl curvature in any dimension. In particular, there is a generalization of Tachibana's theorem for non-negative curvature operator. The key…

In this paper, two things are done. (i) Using cohomological techniques, we explore the consistent deformations of linearized conformal gravity in 4 dimensions. We show that the only possibility involving no more than 4 derivatives of the…

The long-range gravitational terms associated with tidal forces, frame-dragging effects, and gravitational waves are described by the Weyl conformal tensor, the traceless part of the Riemann curvature that is not locally affected by the…

A non-classical Weyl theory is developed for skew-self-adjoint Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and direct and inverse problems are solved. A Borg-Marchenko type uniqueness…

We apply the theory of Weyl structures for parabolic geometries developed by A. Cap and J. Slovak in to compute, for a quaternionic contact (qc) structure, the Weyl connection associated to a choice of scale, i.e. to a choice of…

In this note we wish to complement some recent work in the cosmological literature concerning the Weyl conformal curvature tensor and its parts. In particular, we shall give a clear-cut definition of the Newtonian limits of electric and…

In this paper, we study the complete gradient Ricci solitons $(M^n, g,f)$ with zero radial Weyl curvature, which means that the interior product of $\nabla f$ with the Weyl tensor $W$ is zero, i.e., $i_{\nabla f}W=0$. We classify completely…

We study the zeros of cross-product of Bessel functions and obtain their approximations, based on which we reduce the eigenvalue counting problem for the Dirichlet Laplacian associated with a planar annulus to a lattice point counting…

Weyl fermions are massless chiral quasiparticles existing in materials known as Weyl semimetals. Topological surface states, associated with the unusual electronic structure in the Weyl semimetals, have been recently demonstrated in linear…

We present a complete algebraic classification for the curvature tensor in Weyl-Cartan geometry, by applying methods of eigenvalues and principal null directions on its irreducible decomposition under the group of global Lorentz…

We prove theorems about the Ricci and the Weyl tensors on generalized Robertson-Walker space-times of dimension $n\ge 3$. In particular, we show that the concircular vector introduced by Chen decomposes the Ricci tensor as a perfect fluid…

This elementary discussion generalizes a Weyl geometry to allow quaternion valued gauge transformations and classical Yang-Mills geometric fields. This development will assume that the symmetric metric tensor is real in some gauge, and will…

We consider almost Riemann solitons $(V,\lambda)$ in a Riemannian manifold and underline their relation to almost Ricci solitons. When $V$ is of gradient type, using Bochner formula, we explicitly express the function $\lambda$ by means of…

In the last few years renewed interest in the 3-tensor potential $L_{abc} $ proposed by Lanczos for the Weyl curvature tensor has not only clarified and corrected Lanczos's original work, but generalised the concept in a number of ways. In…