In this paper, we consider pseudosymmetric Lorentz Sasakian space forms admitting almost $\eta-$Ricci solitons in some curvature tensors. Ricci pseudosymmetry concepts of admits soliton have introduced according to the choice special tensors such as Riemann, concircular, projective, $\mathcal{M-}$projective, $W_{1}$ and $W_{2}.$ Then, again tensor, necessary conditions are given for form be sem...

For any triple (M, g,∇) consisting of a Riemannian manifold and a metric connection with skew-symmetric torsion we introduce an elliptic, second order operator Ω acting on spinor fields. In case of a naturally reductive space and its canonical connection, our construction yields the Casimir operator of the isometry group. Several non-homogeneous geometries (Sasakian, nearly Kähler, cocalibrated...

A quasi–regular Sasakian structure on a manifold L is equivalent to writing L as the unit circle subbundle of a holomorphic Seifert C-bundle over a complex algebraic orbifold (X,∆ = ∑ (1− 1 mi )Di). The Sasakian structure is called positive if the orbifold first Chern class c1(X) − ∆ = −(KX + ∆) is positive. We are especially interested in the case when the Riemannian metric part of the Sasakia...

We prove the existence of Sasakian metrics with positive Ricci curvature on certain highly connected odd dimensional manifolds. In particular, we show that manifolds homeomorphic to the 2k-fold connected sum of S × S admit Sasakian metrics with positive Ricci curvature for all k. Furthermore, a formula for computing the diffeomorphism types is given and tables are presented for dimensions 7 and...

We consider generic toric Tri-Sasakian 7-manifolds X7 in the context of Mtheory on AdS4 × X7 and study their AdS/CFT correspondence to N = 3 SCFT in 3D spacetime. We obtain volumes of Tri-Sasakian manifolds and their supersymmetric 5-cycles via cohomological integration technique, and use this to calculate conformal dimensions of baryonic operators in the SCFT side. We also propose quiver-type ...

We construct exact solutions of the Einstein-Dirac equation, which couples the gravitational eld with an eigenspinor of the Dirac operator via the energy-momentum tensor. For this purpose we introduce a new eld equation generalizing the notion of Killing spinors. The solutions of this spinor eld equation are called weak Killing spinors (WK-spinors). They are special solutions of the Einstein-Di...