Para-tt*-bundles on the tangent bundle of an almost para-complex manifold |
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Authors: | Lars Schäfer |
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Institution: | 1. Department Mathematik, Universit?t Hamburg, Bundesstra?e 55, D-20146, Hamburg, Germany
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Abstract: | 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 ${\nabla=D + S}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 induced by the one-parameter family of connections given by and prove a uniqueness result for solutions with a para-complex connection D. Flat nearly para-K?hler 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 , respectively, into SO
0(n,n)/U
π(C
n
), where U
π(C
n
) is the para-complex analogue of the unitary group.
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Keywords: | Para-tt*-geometry and para-tt*-bundles Special para-complex and special para-K?hler manifolds Nearly para-K?hler manifolds Para-pluriharmonic maps Pseudo-Riemannian symmetric spaces |
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