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...

A version of Lichnerowicz’ theorem giving a lower bound of the eigenvalues of the sub-Laplacian under a lower bound on the Sp(1)Sp(1) component of the qc-Ricci curvature on a compact seven dimensional quaternionic contact manifold is established. It is shown that in the case of a seven dimensional compact 3-Sasakian manifold the lower bound is reached if and only if the quaternionic contact man...

We show that #9(S 2 S 3) admits an 8-dimensional complex family of inequivalent non-regular Sasakian-Einstein structures. These are the rst known Einstein metrics on this 5-manifold. In particular, the bound b 2 (M)8 which holds for any regular Sasakian-Einstein M does not apply to the non-regular case. We also discuss the failure of the Hitchin-Thorpe inequality in the case of 4-orbifolds and ...

Copyright q 2010 Siraj Uddin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We study warped product Pseudo-slant submanifolds of Sasakian manifolds. We prove a theorem for the existence of warped product submanifolds of a ...

It is proved that for a non-Sasakian η-Einstein (κ, μ)-manifold M the following three conditions are equivalent: (a) M is flat and 3-dimensional, (b) M is Ricci-semisymmetric, and (c) M is ξ-Riccisemisymmetric. Then it is proved that an ξ-Ricci-semisymmetric (κ, μ)manifold M is either flat and 3-dimensional, or locally isometric to E × S(4), or an Einstein-Sasakian manifold. Mathematics Subject...

We prove that the dimension of the 1-nullity distributionN(1) on a closed Sasakianmanifold M of rank l is at least equal to 2l−1 provided thatM has an isolated closed characteristic. The result is then used to provide some examples ofK-contact manifolds which are not Sasakian. On a closed, 2n+ 1-dimensional Sasakian manifold of positive bisectional curvature, we show that either the dimension o...

The object of this paper is to study invariant submanifoldsM of Sasakian manifolds ̃ M admitting a semisymmetric nonmetric connection, and it is shown that M admits semisymmetric nonmetric connection. Further it is proved that the second fundamental forms σ and σ with respect to Levi-Civita connection and semi-symmetric nonmetric connection coincide. It is shown that if the second fundamental fo...