Related papers: On infinitesimal Einstein deformations

It is known that the moduli space of Einstein structures in four dimensions is generally considered to be rigid so that Einstein metrics tend to be isolated modulo diffeomorphisms under infinitesimal Einstein deformations. We examine the…

This paper initiates the study of the Einstein equation on homogeneous supermanifolds. First, we produce explicit curvature formulas for graded Riemannian metrics on these spaces. Next, we present a construction of homogeneous…

This paper makes a formal study of asymptotically hyperbolic Einstein metrics given, as conformal infinity, a conformal manifold with boundary. The space on which such an Einstein metric exists thus has a finite boundary in addition to the…

We study the deformability of the symmetric Einstein metrics on the spaces $\mathrm{SU}(n)/\mathrm{SO}(n)$ and $\mathrm{SU}(2n)/\mathrm{Sp}(n)$, thereby concluding the problem to second order for all irreducible symmetric spaces. The…

This article describes some geometric invariants and conformal anomalies for conformally compact Einstein manifolds and their minimal submanifolds which have recently been discovered via the Anti-de Sitter/Conformal Field Theory…

We study Einstein riemannian manifolds endowed with a warped product structure. We focus on the case in which both the base and the fiber are Einstein manifolds and establish necessary and sufficient conditions for the warped product itself…

We consider deformations of the scalar curvature of a partially integrable pseudohermitian manifold, in analogy with the work of Fischer and Marsden on Riemannian manifolds. In particular, we introduce and discuss $R$-singular spaces, give…

In this paper we show that a compact warped product Einstein manifold with vanishing Bach tensor of dimension $n \geq 4$ is a finite quotient of a warped product with $(n-1)$-dimensional Einstein fiber. The fiber has constant curvature if…

We study pseudo-Riemannian Einstein manifolds which are conformally equivalent with a metric product of two pseudo-Riemannian manifolds. Particularly interesting is the case where one of these manifolds is 1-dimensional and the case where…

Indefinite Kaehler solutions of the Einstein equations are studied, and it is almost completely determined which compact complex surfaces admit such metrics.

Let $M=G/K$ be a generalized flag manifold, that is the adjoint orbit of a compact semisimple Lie group $G$. We use the variational approach to find invariant Einstein metrics for all flag manifolds with two isotropy summands. We also…

The purpose of this note is to provide some volume estimates for Einstein warped products similar to a classical result due to Calabi and Yau for complete Riemannian manifolds with nonnegative Ricci curvature. To do so, we make use of the…

The linear stability of warped product Einstein metrics as fixed points of the Ricci flow is investigated. We generalise the results of Gibbons, Hartnoll and Pope and show that in sufficiently low dimensions, all warped product Einstein…

We construct explicitly deformations of Einstein's theory of gravity that are consistent and phenomenologically viable since they respect, in particular, cosmological backgrounds. We show that these deformations have unique symmetries in…

We continue the study of the Einstein constraint equations on compact manifolds with boundary initiated by Holst and Tsogtgerel. In particular, we consider the full system and prove existence of solutions in both the near-CMC and…

In this paper, we establish compactness results of some class of conformally compact Einstein 4-manifolds. In the first part of the paper, we improve the earlier results obtained by Chang-Ge. In the second part of the paper, as…

We discuss smooth metric measure spaces admitting two weighted Einstein representatives of the same weighted conformal class. First, we describe the local geometries of such manifolds in terms of certain Einstein and quasi-Einstein warped…

We present a global conformal invariant on closed six-manifolds which obstructs the existence of a conformally Einstein metric. We show that this obstruction is nontrivial and, up to multiplication by a constant, is the unique such…

We prove that various spaces of constrained positive scalar curvature metrics on compact 3-manifolds with boundary, when not empty, are contractible. The constraints we mostly focus on are given in terms of local conditions on the mean…

In this paper we study the Minkowskian product Finsler manifolds. More precisely, we prove that if the Minkowskian product Finsler manifold is Einstein then either the product manifold is Ricci flat or both the quotient manifolds are…