A note on tt *-bundles over compact nearly Kähler manifolds

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Autor/in:
Erscheinungsjahr:
2007
Medientyp:
Text
Schlagworte:
  • Generalized pluriharmonic maps
  • Higgs-bundles and harmonic bundles
  • Nearly Kähler manifolds
  • Special Kähler manifolds
  • tt*-Geometry
Beschreibung:
  • First, we generalize a rigidity result for harmonic maps of Gordon (Gordon (1972) Proc AM Math Soc 33: 433-437) to generalized pluriharmonic maps. We give the construction of generalized pluriharmonic maps from metric tt*-bundles over nearly Kähler manifolds. An application of the last two results is that any metric tt*-bundle over a compact nearly Kähler manifold is trivial (Theorem A). This result we apply to special Kähler manifolds to show that any compact special Kähler manifold is trivial. This is Lu's theorem (Lu (1999) Math Ann 313: 711-713) for the case of compact special Kähler manifolds. Further we introduce harmonic bundles over nearly Kähler manifolds and study the implications of Theorem A for tt*-bundles coming from harmonic bundles over nearly Kähler manifolds. © 2007 Springer Science + Business Media B.V.
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  • info:eu-repo/semantics/closedAccess
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Forschungsinformationssystem der UHH
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oai:www.edit.fis.uni-hamburg.de:publications/d4bffc65-6ebd-4776-a25b-3681eda6b55d