Para-tt*-bundles on the tangent bundle of an almost para-complex manifold

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2006

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In this paper we study para-tt *-bundles (TM, D, S) on the tangent bundle of an almost para-complex manifold (M, τ). We characterise those para-tt *-bundles with ∇ = D + S} induced by the one-parameter family of connections given by ∇ θ = exp(θ τ) ̊ ∇ ̊ exp(-θ τ) and prove a uniqueness result for solutions with a para-complex connection D. Flat nearly para-Kähler manifolds and special para-complex manifolds are shown to be such solutions. We analyse which of these solutions admit metric or symplectic para-tt *-bundles. Moreover, we give a generalisation of the notion of a para-pluriharmonic map to maps from almost para-complex manifolds (M, τ) into pseudo-Riemannian manifolds and associate to the above metric and symplectic para-tt *-bundles generalised para-pluriharmonic maps into Sp(ℝ2n)/Uπ (Cn), respectively, into SO0(n,n)/Uπ (C n ), where Uπ(Cn ) is the para-complex analogue of the unitary group. © 2006 Springer Science + Business Media B.V.

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