Related papers: Deformations and Einstein metrics I

A Riemannian manifold $(M,\rho)$ is called Einstein if the metric $\rho$ satisfies the condition $\Ric (\rho)=c\cdot \rho$ for some constant $c$. This paper is devoted to the investigation of $G$-invariant Einstein metrics with additional…

A simple mapping procedure is presented by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed directly into those in curved space with torsion. Our procedure evolved from…

The classification of homogeneous compact Einstein manifolds in dimension six is an open problem. We consider the remaining open case, namely left-invariant Einstein metrics $g$ on $G = \mathrm{SU}(2) \times \mathrm{SU}(2) = S^3 \times…

The two-jet of the curvature tensor at some point of a pseudo-Riemannian manifold is called Einstein if the Ricci tensor is a multiple of the metric tensor at the given point and additionally its first two covariant derivatives vanish…

Let $X$ be a Fano manifold of dimension at least $2$ and $D$ be a smooth divisor in a multiple of the anticanonical class, $\frac1\alpha(-K_X)$ with $\alpha>1$. It is well-known that K\"ahler-Einstein metrics on $X$ with conic singularities…

In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. We call such a manifold rigid if the universal cover of the base is Einstein or is isometric to a product of Einstein manifolds. When the…

This paper was withdrawn by the author due to an error in the proof of the main result; essentially the parameter R used in the proof may depend on the manifold (M, g), not just on dimension and pinching constant.

The unique Nature of the Lorentz group in four dimensions is the root cause of the many remarkable properties of the Einstein spacetimes, in particular their operational structure on the 2-forms. We show how this operational structure can…

Using the Dirac constraint formalism, we examine the canonical structure of the Einstein-Hilbert action $S_d = \frac{1}{16\pi G} \int d^dx \sqrt{-g} R$, treating the metric $g_{\alpha\beta}$ and the symmetric affine connection…

Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably related, we give an explicit construction of a Poincar\'e-Einstein (pseudo-)metric with conformal infinity the conformal class of the product of the initial metrics.…

We construct a model for noncommutative gravity in four dimensions, which reduces to the Einstein-Hilbert action in the commutative limit. Our proposal is based on a gauge formulation of gravity with constraints. While the action is metric…

We exploit an interpretation of gravity as the symmetry broken phase of a de Sitter gauge theory to construct new solutions to the first order field equations. The new solutions are constructed by performing large $Spin(4,1)$ gauge…

We prove that any compact complex surface with positive first Chern class admits an Einstein metric which is conformally related to a Kaehler metric. The key new ingredient is the existence of such a metric on the blow-up of the complex…

We classify the metric-affine theories of gravitation, in which the metric and the connections are treated as independent variables, by use of several constraints on the connections. Assuming the Einstein-Hilbert action, we find that the…

We study the following problem: given an Einstein metric on a manifold, characterize and study all Einstein metrics which are pointwise projective to the given one. By definition, two metrics are said to be pointwise projectively related if…

We consider invariant Einstein metrics on the Stiefel manifold $V_q\bb{R} ^n$ of all orthonormal $q$-frames in $\bb{R}^n$. This manifold is diffeomorphic to the homogeneous space $\SO(n)/\SO(n-q)$ and its isotropy representation contains…

We show that under some natural geometric assumption, Einstein metrics on conformal products of two compact conformal manifolds are warped product metrics.

In this work, Einstein's view of geometry as physical geometry is taken into account in the analysis of diverse issues related to the notions of inertial motion and inertial reference frame. Einstein's physical geometry enables a…

Let $G$ be a simple compact connected Lie group. We study homogeneous Einstein metrics for a class of compact homogeneous spaces, namely generalized flag manifolds $G/H$ with second Betti number $b_{2}(G/H)=1$. There are 8 infinite families…

It is shown that given an analytic Lorentzian metric on a 4-manifold, $g$, which admits two Killing vector fields, then it exists a local deformation law $\eta = a g + b H$, where $H$ is a 2-dimensional projector, such that $\eta$ is flat…