A canonical structure on the tangent bundle of a pseudo- or para-kähler manifold

HIGHLIGHTS

• who: Henri Anciaux and Pascal Romon from the It is a classical fact that given any differentiable manifold M, its cotangent bundle T * M enjoys a canonical symplectic structure Ω* Moreover, given a linear connection ∇ on a manifold M, (e_g the Levi-Civita connection of a Riemannian metric), the bundle T T M splits into a direct sum of two subbundles HM and V M, both isomorphic to T M. This allows to define an almost complex structure J by setting J(Xh, Xv ) :=(-Xv, Xh ), where, for X ∈ T T M=HM ⊕ V M, we write X . . .
  

   

  

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