Related papers: Remarks on $\eta$-Einstein unit tangent bundles

The main purpose of the paper is to prove that if a compact Riemannian manifold admits a gradient $\rho$-Einstein soliton such that the gradient Einstein potential is a non-trivial conformal vector field, then the manifold is isometric to…

This paper derives a sufficient condition for the existence of cohomogeneity one Einstein metrics on double disk bundles of two summands type. The condition is an inequality that involves geometric data from the principal orbits.

The conditions under which a given manifold $M$ may be given a tangent bundle or a cotangent bundle structure are analyzed. This is an important property arising in different contexts. For instance, in the study of integrability of a given…

A unification model for strong, electromagnetic, weak and gravitational forces is proposed. The tangent space of ordinary coordinate 4-dimensional spacetime is a submanifold of an 14-dimensional internal spacetime spanned by four frame…

The difference tensor C.R - R.C of Einstein manifolds, some quasi-Einstein manifolds and Roter type manifolds, of dimension n > 3, satisfy the following curvature condition: (A) C.R - R.C = Q(S,C) - (k /(n-1)) Q(g,C). We investigate…

We prove an asymptotic bound on the eta invariant of a family of coupled Dirac operators on an odd dimensional manifold. In the case when the manifold is the unit circle bundle of a positive line bundle over a complex manifold, we obtain…

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…

We find the necessary conditions for a sequential warped product manifold to be a quasi-Einstein manifold. We also investigate the necessary and sufficient conditions for a sequential standard static space-time and a sequential generalized…

Einstein Gravity can be formulated as a gauge theory with the tangent space respecting the Lorentz symmetry. In this paper we show that the dimension of the tangent space can be larger than the dimension of the manifold and by requiring the…

We prove that any compact selfdual Einstein 4-orbifold of positive scalar curvature whose isometry group contains a 2-torus is, up to an orbifold covering, a quaternion Kaehler quotient of (k-1)-dimensional quaternionic projective space by…

In this note, we find the conditions on an odd-dimensional Riemannian manifolds under which its twistor space is eta-Einstein.

We construct examples of four dimensional manifolds with Spin$^c$-structures, whose moduli spaces of solutions to the Seiberg-Witten equations, represent a non-trivial bordism class of positive dimension, i.e. the Spin$^c$-structures are…

This paper studies the two-component spinor form of massive spin-3/2 potentials in conformally flat Einstein four-manifolds. Following earlier work in the literature, a non-vanishing cosmological constant makes it necessary to introduce a…

We show that any quantum irreducible flag manifold satisfies an analogue of the Einstein condition, expressing proportionality between the Ricci tensor and the metric, at least in a small open interval around the classical value of the…

We consider sphere bundles P and P' of totally null planes of maximal dimension and opposite self-duality over a 4-dimensional manifold equipped with a Weyl or Riemannian geometry. The fibre product PP' of P and P' is found to be…

We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products…

The anti-self-dual projection of the spin connections of certain four-dimensional Einstein manifolds can be Abelian in nature. These configurations signify bundle reductions. By a theorem of Kobayashi and Nomizu such a process is predicated…

Einstein like $(\varepsilon)$-para Sasakian manifolds are introduced. For an $(\varepsilon) $-para Sasakian manifold to be Einstein like, a necessary and sufficient condition in terms of its curvature tensor is obtained. The scalar…

On a compact n-dimensional manifold, it has been conjectured that a critical point metric of the total scalar curvature, restricted to the space of metrics with constant scalar curvature of unit volume, will be Einstein. This conjecture was…

Let $(M,g)$ be a Riemannian manifold, $L(M)$ its frame bundle. We construct new examples of Riemannian metrics on $L(M)$, which are obtained from Riemannian metrics on the tangent bundle $TM$. We compute the Levi--Civita connection and…