The object of the present paper is to study generalized -recurrent Sasakian manifolds. Here it is proved that a generalized -recurrent Sasakian manifold is an Einstein manifold. We also find a relation between the associated 1-forms A and B for a generalized -recurrent and generalized concircular -recurrent Sasakian manifolds. Finally, we proved that a three dimensional locally generalized -rec...

The hidden symmetries of higher dimensional Kerr-NUT-(A)dS metrics are investigated. In certain scaling limits these metrics are related to the Einstein–Sasaki ones. The complete set of Killing–Yano tensors of the Einstein–Sasaki spaces are presented. For this purpose the Killing forms of the Calabi–Yau cone over the Einstein–Sasaki manifold are constructed. Two new Killing forms on Einstein–Sa...

The logic stretch that Relativity has imposed was caused by the alteration of length perception that Einstein forced to introduce in order to accommodate time in a four dimensional orthogonal manifold. Because no space and time can be both at once “absolute”, Einstein changed both definitions in order to keep light’s velocity that was derived by space and time invariant. This was a mistake in l...

The object of this paper is to study (k, μ)-paracontact metric manifolds with qusi-conformal curvature tensor. It has been shown that, h-quasi conformally semi-symmetric and φ-quasi-conformally semi-symmetric (k, μ)-paracontact metric manifold with k 6= −1 cannot be an η-Einstein manifold.

Which smooth compact n-manifolds admit Riemannian metrics of constant Ricci curvature? A direct variational approach sheds some interesting light on this problem, but by no means answers it. This article surveys some recent results concerning both Einstein metrics and the associated variational problem, with the particular aim of highlighting the striking manner in which the 4-dimensional case ...

Which smooth compact 4-manifolds admit an Einstein metric with non-negative Einstein constant? A complete answer is provided in the special case of 4-manifolds that also happen to admit either a complex structure or a symplectic structure. A Riemannian manifold (M, g) is said to be Einstein if it has constant Ricci curvature, in the sense that the function v −→ r(v, v) on the unit tangent bundl...

It is proved that any compact almost Kähler, Einstein 4-manifold whose fundamental form is a root of the Weyl tensor is necessarily Kähler.

Some results on the properties of T -flat, quasiT -flat,  T -flat,  T -flat, T -semi-symmetric,  T Ricci recurrent and T - -recurrent LP-Sasakian manifolds are obtained. It is also proved that an LP-Sasakian manifold satisfying the condition T . 0 S  is an  -Einstein manifold. MSC 2000. 53C15, 53C25, 53C50, 53D15.

We study compactification of five dimensional ungauged N = 2 supergravity coupled to vectorand hypermultiplets on orbifold S/Z2. In the model, the vector multiplets scalar manifold is arbitrary while the hypermultiplet scalars span a generalized self dual Einstein manifold constructed by Calderbank and Pedersen. The bosonic and the fermionic sectors of the low energy effective N = 1 supergravit...

Let (M4, g, ω) be a compact, almost-Kähler Einstein manifold of negative star-scalar curvature. Then (M,ω) is a minimal symplectic 4-manifold of general type. In particular, M cannot be differentiably decomposed as a connected sum N#CP2.