Related papers: 3-Sasakian Geometry, Nilpotent Orbits, and Excepti…
We analyze the classic problem of existence of Einstein metrics in a given conformal structure for the class of conformal structures inducedf Nurowski's construction by (oriented) (2,3,5) distributions. We characterize in two ways such…
We give new examples of compact, negatively curved Einstein manifolds of dimension $4$. These are seemingly the first such examples which are not locally homogeneous. Our metrics are carried by a sequence of 4-manifolds $(X_k)$ previously…
We holographically study supersymmetric deformations of $N=3$ and $N=1$ superconformal field theories (SCFTs) in three dimensions using four-dimensional $N=4$ gauged supergravity coupled to three-vector multiplets with non-semisimple…
This paper is concerned with the construction of special metrics on non-compact 4-manifolds which arise as resolutions of complex orbifold singularities. Our study is close in spirit to the construction of the hyperkaehler gravitational…
The Darboux-Koenigs metrics in 2D are an important class of conformally flat, non-constant curvature metrics with a single Killing vector and a pair of quadratic Killing tensors. In [arXiv:1804.06904] it was shown how to derive these by…
We investigate the geometry of closed, orientable, hyperbolic $3$-manifolds whose fundamental groups are $k$-free for a given integer $k\ge 3$. We show that any such manifold $M$ contains a point $P$ of $M$ with the following property: If…
In the present work some examples of toric hyperkahler metrics in eight dimensions are constructed. First it is described how the Calderbank-Pedersen metrics arise as a consequence of the Joyce description of selfdual structures in four…
We analyze a 1-parameter family of heart shape and a 3-parameter family obtained by gluing three footballs, both of which are examples of reducible spherical conical metrics. For these examples we verify the structure theorem given in [15]…
In this paper, we obtain new non-singular Einstein-Sasaki spaces in dimensions D\ge 7. The local construction involves taking a circle bundle over a (D-1)-dimensional Einstein-Kahler metric that is itself constructed as a complex line…
We are proposing a new Ricci flat metric constructed from an infinite family of Sasaki-Einstein, $Y^{(p,q)}$, geometries. This geometry contains a free parameter $s$ and in the $s\to 0$ limit we get back the usual CY. When this geometry is…
In this paper we investigate the possibility to obtain locally new Sasaki-Einstein metrics on the space $T^{1,1}$ considering a deformation of the standard metric tensor field. We show that from the geometric point of view this deformation…
The link between 3D spaces with (in general, non-constant) curvature and quantum deformations is presented. It is shown how the non-standard deformation of a sl(2) Poisson coalgebra generates a family of integrable Hamiltonians that…
We use the recipe of arXiv:1003.2974 to find half-BPS near-horizon geometries in the t$^3$ model of $N=2$, $D=4$ gauged supergravity, and explicitely construct some new examples. Among these are black holes with noncompact horizons, but…
We show that any toric K\"ahler cone with smooth compact cross-section admits a family of Calabi-Yau cone metrics with conical singularities along its toric divisors. The family is parametrized by the Reeb cone and the angles are given…
A detailed study is made of the noncommutative geometry of $R^3_q$, the quantum space covariant under the quantum group $SO_q(3)$. For each of its two $SO_q(3)$-covariant differential calculi we find its metric, the corresponding frame and…
We prove that any totally geodesic hypersurface $N^5$ of a 6-dimensional nearly K\"ahler manifold $M^6$ is a Sasaki-Einstein manifold, and so it has a hypo structure in the sense of \cite{ConS}. We show that any Sasaki-Einstein 5-manifold…
In this paper we introduce the concept of $(\varepsilon)$-almost paracontact manifolds, and in particular, of $(\varepsilon)$-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci…
We prove a volume inequality for 3-manifolds having C^0 metrics "bent" along a hypersurface, and satisfying certain curvature pinching conditions. The result makes use of Perelman's work on Ricci flow and geometrization of closed…
We survey some of our recent results on length series identities for hyperbolic (cone) surfaces, possibly with cusps and/or boundary geodesics; classical Schottky groups; representations/characters of the one-holed torus group to $SL(2,…
This is a collection of notes on the properties of left-invariant metrics on the eight-dimensional compact Lie group SU(3). Among other topics we investigate the existence of invariant pseudo-Riemannian Einstein metrics on this manifold. We…