Related papers: Static Ricci-flat 5-manifolds admitting the 2-sphe…
We derive formulas for variations of mass, angular momentum and canonical energy in Einstein (n-2)-gauge form field theory by means of the ADM formalism. Considering the initial data for the manifold with an interior boundary which has the…
The effective action of $N=2$, $d=4$ supergravity is shown to acquire no quantum corrections in background metrics admitting super-covariantly constant spinors. In particular, these metrics include the Robinson-Bertotti metric (product of…
We classify Einstein metrics on $\mathbb{R}^4$ invariant under a four-dimensional group of isometries including a principal action of the Heisenberg group. The metrics are either Ricci-flat or of negative Ricci curvature. We show that all…
In this note, we complete the classification of the geometry of non-compact two-dimensional gradient Ricci solitons. As a consequence, we obtain two corollaries: First, a complete two-dimensional gradient Ricci soliton has bounded…
We find an obstruction to the existence of non-singular solutions to the normalized Ricci flow on four-manifolds with $b^+=1$. By using this obstruction, we study the relationship between the existence or non-existence of non-singular…
In this article, we shall investigate the relationship between the existence or non-existence of non-singular solutions to the normalized Ricci flow and smooth structures on closed 4-manifolds, where non-singular solutions to the normalized…
We consider Riemannian 4-manifolds that Gromov-Hausdorff converge to a lower dimensional limit space, with the Ricci tensor going to zero. Among other things, we show that if the limit space is two dimensional then under some mild…
Important models for immortal solutions of Ricci flow that collapse with bounded curvature come from locally G-invariant solutions on principal bundles, where G is a nilpotent Lie group. In this paper, we establish convergence and…
Ricci-like solitons on Sasaki-like almost contact B-metric manifolds are the object of study. Cases, where the potential of the Ricci-like soliton is the Reeb vector field or pointwise collinear to it, are considered. In the former case,…
Using a solution generating technique based on the symmetries of the dimensionally reduced Lagrangian we derive two exact solutions of the Einstein-Maxwell-Dilaton field equations in five dimensions. More specifically, these solutions…
The Zipoy-Voorhees family of static, axisymmetric vacuum solutions forms an interesting family in that it contains the Schwarzschild black hole excepting which all other members have naked singularity. We analyze some properties of the…
We consider new cosmological solutions which generalize the cosmological patch of the Anti-de Sitter (AdS) space-time, allowing for fluids with equations of state such that $w\neq -1$. We use them to derive the associated full manifolds. We…
We describe an extension of the axioms of quantization to the case of 2-plectic manifolds. We show how such quantum spaces can be obtained as stable classical solutions in a zero-dimensional 3-algebra reduced model obtained by dimensional…
Gradient steady Ricci solitons are natural generalizations of Ricci-flat manifolds. In this article, we prove a curvature gap theorem for gradient steady Ricci solitons with nonconstant potential functions; and a curvature gap theorem for…
We show that a polarized affine variety admits a Ricci flat K\"ahler cone metric, if and only if it is K-stable. This generalizes Chen-Donaldson-Sun's solution of the Yau-Tian-Donaldson conjecture to K\"ahler cones, or equivalently,…
We determine all asymptotically flat, supersymmetric and biaxisymmetric soliton and black hole solutions to five dimensional minimal supergravity. In particular, we show that the solution must be a multi-centred solution with a…
We present an asymptotically flat and stationary multi-black lens solution with bi-axisymmetry of $U(1)\times U(1)$ as a supersymmetric solution in the five-dimensional minimal ungauged supergravity. We show that the spatial cross section…
In this work we perform a general study of properties of a class of locally symmetric embedded hypersurfaces in spacetimes admitting a $1+1+2$ spacetime decomposition. The hypersurfaces are given by specifying the form of the Ricci tensor…
We study a class of two-dimensional compact extra spaces isomorphic to the sphere $S^2$ in the framework of multidimensional gravitation. We show that there exists a family of stationary metrics that depend on the initial (boundary)…
We consider the classification of static near-horizon geometries of stationary extremal (not necessarily BPS) black hole solutions of five dimensional Einstein-Maxwell theory coupled to a Chern-Simons term with coupling xi (with xi=1…