Related papers: Conformal Collineations and Ricci Inheritance Symm…
In this work, we study nonconformally Ricci-flat gravitational instantons in four-dimensional Conformal Gravity, both in vacuum and in the presence of nonlinear conformal matter. First, the one-parameter extension of the Kerr-NUT-AdS metric…
In this paper, we present a complete classification of Locally Rotationally Symmetric (LRS) Bianchi type I spacetimes according to their Conformal Ricci Collineations (CRCs). When the Ricci tensor is non-degenerate, a general form of the…
In this paper we prove localised weighted curvature integral estimates for solutions to the Ricci flow in the setting of a smooth four dimensional Ricci flow or a closed $n$-dimensional K\"ahler Ricci flow. These integral estimates improve…
This book gives an introduction to fundamental aspects of generalized Riemannian, complex, and K\"ahler geometry. This leads to an extension of the classical Einstein-Hilbert action, which yields natural extensions of Einstein and…
It is shown that bounds of all orders of derivative would follow from uniform bounds for the metric and the torsion 1-form, for a flow in non-K\"ahler geometry which can be interpreted as either a flow for the Type IIB string or the Anomaly…
In this paper, we first apply an integral identity on Ricci solitons to prove that closed locally conformally flat gradient Ricci solitons are of constant sectional curvature. We then generalize this integral identity to complete noncompact…
There are described equations for a pair comprising a Riemannian metric and a Killing field on a surface that contain as special cases the Einstein Weyl equations (in the sense of D. Calderbank) and a real version of a special case of the…
We study the breakdown of conformal symmetry in a conformally invariant gravitational model. The symmetry breaking is introduced by defining a preferred conformal frame in terms of the large scale characteristics of the universe. In this…
We study conformal field theory on two-dimensional orbifolds and show this to be an effective way to analyze physical effects of geometric singularities with angular deficits. They are closely related to boundaries and cross caps.…
Ricci solitons are natural generalizations of Einstein metrics. They are also special solutions to Hamilton's Ricci flow and play important roles in the singularity study of the Ricci flow. In this paper, we survey some of the recent…
Radar-holonomic congruences of wordlines are proposed as a weaker substitute for the too restrictive class of Born-rigid motions. The definition is expressed as a set of differential equations. Integrability conditions and Cauchy data are…
We show that grains streaming through a fluid are generically unstable if their velocity, projected along some direction, matches the phase velocity of a fluid wave (linear oscillation). This can occur whenever grains stream faster than any…
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
We present a conformally invariant generalized form of the free particle action by connecting the wave and particle aspects through gravity. Conformal invariance breaking is introduced by choosing a particular configurat$ of dynamical…
We consider a class of spin systems on randomly triangulated surfaces as discrete approximations to conformal matter fields coupled to 2d gravity. On the basis of certain universality assumptions we argue that at critical points with…
We study the behavior of the normalized Ricci flow of invariant Riemannian homogeneous metrics at infinity for generalized Wallach spaces, generalized flag manifolds with four isotropy summands and second Betti number equal to one, and the…
Conformal invariance plays a significant role in many areas of Physics, such as conformal field theory, renormalization theory, turbulence, general relativity. Naturally, it also plays an important role in geometry: theory of Riemannian…
Based upon the formalism of conformal field theory with a boundary, we give a description of the boundary effect on fully developed two dimensional turbulence. Exact one and two point velocity correlation functions and energy power spectrum…
We consider the Ricci flow equation for invariant metrics on compact and connected homogeneous spaces whose isotropy representation decomposes into two irreducible inequivalent summands. By studying the corresponding dynamical system, we…
We define two conformal structures on $S^1$ which give rise to a different view of the affine curvature flow and a new curvature flow, the ``$Q$-curvature flow". The steady state of these flows are studied. More specifically, we prove four…