arXiv research

The study classifies quasi-Einstein manifolds with constant scalar curvature.

Compact quasi-Einstein metrics with constant scalar curvature are locally homogeneous in 3D.

Linearized Einstein equations simplified via Calabi operator.

Compact Einstein manifolds with specific curvature operators are constant curvature spaces.

Classifies weakly Einstein hypersurfaces in spaces of constant curvature.

Study rigidifies Einstein-type manifolds with boundary and constant curvature.

Bismut Einstein metrics on complex manifolds are Kähler Einstein or Bismut Ricci flat.

Sasakian immersions prove Sasaki-Ricci solitons are η-Einstein with rational constants.

The paper studies $m$-quasi Einstein manifolds with convex potential and finds constant scalar curvature.

We obtain a Kaehler Einstein structure on the nonzero cotangent bundle of a Riemannian manifold of positive constant sectional curvature. The obtained Kaehler Einstein structure cannot have constant holomorphic sectional curvature and is not locally symmetric.

Study Dirac-Einstein equations on manifolds with boundary, focusing on constant volume and chiral conditions.

New findings on static near horizon geometries and quasi-Einstein manifolds, including rigidity results for negative cosmological constant.

We obtain a locally symmetric Kaehler Einstein structure on the cotangent bundle of a Riemannian manifold of negative constant sectional curvature. Similar results are obtained on a tube around zero section in the cotangent bundle, in the case of a Riemannian manifold of positive constant sectional curvature. The obtai…

Simplified Obata-Vétois argument for Einstein manifolds with nonnegative scalar curvature.

We obtain a locally symmetric Kaehler Einstein structure on a tube in the nonzero cotangent bundle of a Riemannian manifold of positive constant sectional curvature. The obtained Kaehler Einstein structure cannot have constant holomorphic sectional curvature.

Characterizes warping functions in Einstein Poisson warped spaces.

We prove nonlinear stability for a large class of solutions to the Einstein equations with a positive cosmological constant and compact spatial topology in arbitrary dimensions, where the spatial metric is Einstein with either positive or negative Einstein constant. The proof uses the CMC Einstein flow and stability fo…

We derive some elliptic differential inequalities from the Weitzenböck formulas for the traceless Ricci tensor of a Kähler manifold with constant scalar curvature and the Bochner tensor of a Kähler-Einstein manifold respectively. Using elliptic estimates and maximum principle, some $L^p$ and $L^\infty$ pinching result…

We study Einstein's equation in $(m+n)D$ and $(1+n)D$ warped spaces $(\bar{M},\bar{g})$ and classify all such spaces satisfying Einstein equations $\bar{G}=-\barΛ\bar{g}$. We show that the warping function not only can determine the cosmological constant $\barΛ$ but also it can determine the cosmological constant $Λ$ a…

The paper proves conditions for Kähler-Einstein metrics to remain Kähler-Einstein under cscK perturbations.

The study explores metrics with constant curvature on compact manifolds.

We obtain a class of Kaehler Einstein structures on the nonzero cotangent bundle of a Riemannian manifold of positive constant sectional curvature. The obtained class of Kaehler Einstein structure depends on one essential parameter, cannot have constant holomorphic sectional curvature and is not locally symmetric.

We obtain a class of locally symetric Kaehler Einstein structures on the nonzero cotangent bundle of a Riemannian manifold of positive constant sectional curvature. The obtained class of Kaehler Einstein structures depends on one essential parameter and cannot have constant holomorphic sectional curvature.

Recently, it is proven that generalized Robertson-Walker space-times in all orthogonal subspaces of Gray's decomposition but one(unrestricted) are perfect fluid space-times. GRW space-times in the unrestricted subspace are identified by having constant scalar curvature. Generalized quasi-Einstein GRW space-times have a…

Paper finds conditions for non-Einstein relative Yamabe metrics.

Global well-posedness and asymptotic convergence for vacuum Einstein's equations proved.

3D Lorentzian manifolds can't be closed Einstein with positive constant.

This paper contains a classification of all 3-dimensional manifolds with constant scalar curvature $S \not= 0$ that carry a non-trivial solution of the Einstein-Dirac equation.

A 5D manifold's rigidity proven for k=3 with constant scalar curvature.

Classification of toric self-dual Einstein gravitational instantons with negative cosmological constant

In this paper we first use the result in $[12]$ to remove the assumption of the $L^2$ boundedness of Weyl curvature in the gap theorem in $[9]$ and then obtain a gap theorem for a class of conformally compact Einstein manifolds with very large renormalized volume. We also uses the blow-up method to derive curvature est…

By using the Hawking Taub-NUT metric, this note gives an explicit construction of a 3-parameter family of Einstein Finsler metrics of non-constant flag curvature in terms of navigation representation.

All anti-self-dual Einstein metrics with non-zero cosmological constant arise from a single second-order PDE.

We give some uniform estimates for constant mean curvature solutions of the conformal vacuum Einstein constraint equations on compact manifolds. Existence of those solutions was given in a paper by J. Isenberg.

We give an elementary treatment of the existence of complete Kahler-Einstein metrics with nonpositive Einstein constant and underlying manifold diffeomorphic to the tangent bundle of the (n+1)-sphere.

Kähler-Ricci solitons can be immersed into complex space forms if and only if the manifold is Einstein.

Study on generalized quasi-Einstein structures in contact geometry.

A formula of the renormalized volume of tubes over polalized Kähler-Einstein manifolds is given in terms of the Einstein constant and the volume of the polarization.

Einstein-Kropina metrics extend Einstein condition to all signatures and classify Finsler gravity solutions.

New decomposable solutions found in 11D supergravity.

The article characterizes gradient ρ-Einstein solitons under specific conditions.

We establish variational formulas for Ricci upper and lower bounds, as well as a derivative formula for the Ricci curvature. As applications, constant curvature manifolds, Einstein manifolds and Ricci parallel manifolds are identified, respectively, with different integral-differential formulas and semigroup inequaliti…

The study finds conditions for Kaehler-Einstein and cscK metrics on certain manifold coverings.

Study on rigidity and characterization of generalized quasi-Einstein manifolds.

The orthogonal decomposition of the Webster curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differential inequalities from the Weitzenböck formulas for the traceless pseudo-Hermitian Ricci tensor and the Chern-Moser tensor of Sasakian manifol…

We construct infinite-dimensional families of non-singular static space times, solutions of the vacuum Einstein-Maxwell equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.

Unique conformal metrics found on certain manifolds.

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 base is three dimensional and the dimension of the fiber is greater than one we sho…