Related papers: Gradient Shrinking Solitons with Vanishing Weyl Te…

The Bach tensor is classically defined in dimension 4, and work from J. Bergman \cite{bergman:2004} and others shows that $B = \frac{1}{2}U + \frac{1}{6}V$ where $U$ and $V$ are more basic 2-tensors, which are symmetric, divergence-free,…

Lorentzian manifolds with vanishing second covariant derivative of the Riemann tensor are studied. Their existence, classification and explicit local expression are considered. Related issues and open questions are briefly commented.

We study black and white hole analogues in Weyl semimetals with inhomogenous nodal tilts. We study how the presence of a microscopic lattice, giving rise to low-energy fermion doubler states at large momenta that are not present for…

We prove a splitting theorem for complete gradient Ricci soliton with nonnegative curvature and establish a rigidity theorem for codimension one complete shrinking gradient Ricci soliton in $\mathbb R^{n+1}$ with nonnegative Ricci…

We prove a local gradient estimate for positive eigenfunctions of $ \mathcal{L} $-operator on conformal solitons given by a general conformal vector field. As an application, we obtain a Liouville type theorem for $ \mathcal{L} u = 0 $,…

In this paper, we derive certain curvature estimates for 4-dimensional gradient steady Ricci solitons either with positive Ricci curvature or with scalar curvature decay.

In this paper, we mainly study gradient $\rho$-Einstein solitons on doubly warped product manifolds. More explicitly, we obtain necessary and sufficient conditions for a doubly warped product manifold to be a gradient $\rho$-Einstein…

We use the theory of isoparametric functions to investigate gradient Ricci solitons with constant scalar curvature. We show rigidity of gradient Ricci solitons with constant scalar curvature under some conditions on the Ricci tensor, which…

In this paper, we study the geometry and topology of complete gradient shrinking Sasaki-Ricci solitons. We first prove that they must be connected at infinity. This is a Sasaki analogue of gradient shrinking K\"ahler-Ricci solitons.…

Necessary conditions for various algebraic types of the Weyl tensor are determined. These conditions are then used to find Weyl aligned null directions for the black ring solution. It is shown that the black ring solution is algebraically…

The problem of characterizing conformally Einstein manifolds by tensorial conditions has been tackled recently in papers by M. Listing, and in work by A. R. Gover and P. Nurowski. Their results apply to metrics satisfying a "non-degeneracy"…

In this paper, we show that steady or shrinking complete gradient Yamabe solitons with finite total scalar curvature and non-positive Ricci curvature are Ricci flat. Moreover, under certain pinching condition for Ricci curvature, we show…

We prove that all ends of a gradient shrinking $\rho$-Einstein soliton are $\varphi$-non-parabolic, provided $\rho$ is nonnegative and the soliton has bounded and nonnegative scalar curvature, where the weight $\varphi$ is a negative…

In this paper we investigate gradient Yamabe solitons, either steady or shrinking, that can be isometrically immersed into space forms as hypersurfaces that admit an upper bound on the norm of their second fundamental form. Those solitons…

In this paper, we completely classify nontrivial non-flat two- and three-dimensional complete gradient Yamabe solitons.

We introduce a scalar invariant on manifolds with density which is analogous to the renormalized volume coefficient $v_3$ in conformal geometry. We show that this invariant is variational and that shrinking gradient Ricci solitons are…

In this paper we introduce discrete gradient methods to discretize irreversible port-Hamiltonian systems showing that the main qualitative properties of the continuous system are preserved using this kind discretizations methods.

We prove the existence of a unique complete shrinking gradient K\"ahler-Ricci soliton with bounded scalar curvature on the blowup of $\mathbb{C}\times\mathbb{P}^{1}$ at one point. This completes the classification of such solitons in two…

In this note we prove that any four-dimensional half conformally flat gradient steady Ricci soliton must be either Bryant's soliton or Ricci flat. We also classify four-dimensional half conformally flat gradient shrinking Ricci solitons…

Algebraically special gravitational fields are described using algebraic and differential invariants of the Weyl tensor. A type III invariant is also given and calculated for Robinson-Trautman spaces.