Search results for "Killing spinor"
showing 2 items of 2 documents
The geometry of N=3 AdS4 in massive IIA
2018
The geometry of the ${\cal N} = 3$, SO(4)--invariant, AdS$_4$ solution of massive type IIA supergravity that uplifts from the ${\cal N} = 3 $ vacuum of $D=4$ ${\cal N} = 8$ dyonic ISO(7) supergravity is investigated. Firstly, a $D=4$, SO(4)--invariant restricted duality hierarchy is constructed and used to uplift the entire, dynamical SO(4)--invariant sector to massive type IIA. The resulting consistent uplift formulae are used to obtain a new local expression for the ${\cal N} = 3 $ AdS$_4$ solution in massive IIA and analyse its geometry. Locally, the internal $S^6$ geometry corresponds to a warped fibration of $S^2$ and a hemisphere of $S^4$. This can be regarded as a warped generalisati…
Manifolds with vectorial torsion
2015
Abstract The present note deals with the properties of metric connections ∇ with vectorial torsion V on semi-Riemannian manifolds ( M n , g ) . We show that the ∇-curvature is symmetric if and only if V ♭ is closed, and that V ⊥ then defines an ( n − 1 ) -dimensional integrable distribution on M n . If the vector field V is exact, we show that the V-curvature coincides up to global rescaling with the Riemannian curvature of a conformally equivalent metric. We prove that it is possible to construct connections with vectorial torsion on warped products of arbitrary dimension matching a given Riemannian or Lorentzian curvature—for example, a V-Ricci-flat connection with vectorial torsion in di…