Citation Context

...X, η+ η) as required (by noting that X ∈ h pairs to zero with u±). This establishes (QH2). THROUGH THE ANALYTIC HALO 15 For (QH3) it is now sufficient to check Ker(ω) ∩ Ker(dµ) = 0 at each point (cf. =-=[1]-=- p.49). Thus choose a point m ∈ M = GAH and a tangent vector X ∈ TmM . Suppose that X ∈ Ker(ω) ∩Ker(dµ). Since X is in the kernel of dµH we have η ′ = 0 (here primes denote derivatives along X , so η′...

Citation Context

...(dϕ−1)∗) : TM → TM, Φ(LM ) = LM . We refer to ϕ as a Dirac diffeomorphism. Remark 5.4. Forward Dirac maps ϕ : M → N satisfying the additional transversality condition ker(dϕ) ∩LM = {0} are studied in =-=[1, 8, 7]-=- in the context of actions and momentum maps. 5.2. Clean intersection and smoothness issues. In the previous subsection, we used pullback and pushforward to obtain two ways to relate Dirac structures ...

Citation Context

...e ∇ is an isotropic splitting with curvature H ∈ Ω3(M). One has that L is integrable⇐⇒ dH(U∇(L)) ⊂ Π∇(Cl(E))U∇(L), (1.17) where dH = d −H ∧ · is the H-twisted differential. We refer to [14] (see also =-=[1]-=-) for a proof. Covariant spinors. The Clifford bundle also has a representation on multi-vector fields. The map Π op ∇ : Cl(E) −→ End (∧ •TM) is given on generators e ∈ E by Π op ∇ (e)X = p(e) ∧ X+ is...