Universal Bochner-Weitzenböck Formulas for Hyper-Kählerian Gradients

  • Yasushi Homma
Part of the Trends in Mathematics book series (TM)


Hyper-Kählerian gradients on hyper-Kähler manifolds are first-order differential operators naturally defined by hyper-Kähler structure. We show that the principal symbols of hyper-Kählerian gradients are related to the enveloping algebra and Casimir elements of the symplectic group. In particular, we give universal Bochner-Weitzenböck formulas which are certain relations in the enveloping algebra. From the formulas, we construct BochnerWeitzenböck formulas for hyper-Kählerian gradients.


Gradients Bochner-Weitzenböck formulas Sp(n)-modules Casimir elements 

Mathematics Subject Classification (2000)

58J60 17B35 53C26 


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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Yasushi Homma
    • 1
  1. 1.Department of Mathematical SciencesWaseda UniversityShinjuku-ku TokyoJapan

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