Abstract The debate on the physical relevance of conformal transformations can be faced by taking the Palatini approach into account to gravitational theories. We show that conformal transformations are not only a mathematical tool to disentangle gravitational and matter degrees of freedom (passing from the Jordan frame to the Einstein frame) but they acquire a physical meaning considering the ...

In this paper we examine a new class of five dimensional (5D) exact solutions in extra dimension gravity possessing Lie algebroid symmetry. The constructions provide a motivation for the theory of Clifford nonholonomic algebroids elaborated in Ref. [1]. Such Einstein–Dirac spacetimes are parametrized by generic off–diagonal metrics and nonholonomic frames (vielbeins) with associated nonlinear c...

The notion of coupled Kähler–Einstein metrics was introduced recently by Hultgren–Witt Nyström. In this paper we discuss deformation a metric on Fano manifold. We obtain necessary and sufficient condition for to be deformed another manifold admitting non-trivial holomorphic vector fields. addition also Käher–Einstein when the complex structure varies.

We analyse in a systematic way the (non-)compact n-dimensional Einstein-Weyl spaces equipped with a cohomogeneity-one metric. In that context, with no compactness hypothesis for the manifold on which lives the Einstein-Weyl structure, we prove that, as soon as the (n-1)-dimensional space is a homogeneous reductive Riemannian space with a unimodular group of left-acting isometries G : • there ex...

Big improvements in the performance of graphics processing units (GPUs) turned them into a compelling platform for high performance computing. In this thesis, we discuss the usage of NVIDIA’s CUDA in two applications – Einstein@Home, a distributed computing software, and OpenSteer, a game-like application. Our work on Einstein@Home demonstrates that CUDA can be integrated into existing applicat...

We analyse in a systematic way the (non-)compact n-dimensional Einstein-Weyl spaces equipped with a cohomogeneity-one metric. In that context, with no compactness hypothesis for the manifold on which lives the Einstein-Weyl structure, we prove that, as soon as the (n-1)-dimensional basis space is an homogeneous reductive Riemannian space with an unimodular group of left-acting isometries G : • ...

In this paper we study the topology of conformally compact Einstein 4-manifolds. When the conformal infinity has positive Yamabe invariant and the renormalized volume is also positive we show that the conformally compact Einstein 4-manifold will have at most finite fundamental group. Under the further assumption that the renormalized volume is relatively large, we conclude that the conformally ...

1 We describe in this paper all simply connected Spin c manifolds carrying parallel and real Killing spinors. In particular we show that every Sasakian manifold (not necessarily Einstein) carries a canonical Spin c structure with Killing spinors.

In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped product structure. This warped product structure will be used to study warped product Einstein structures in [HPW3].