Abstract
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.
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Homma, Y. (2004). Universal Bochner-Weitzenböck Formulas for Hyper-Kählerian Gradients. In: Qian, T., Hempfling, T., McIntosh, A., Sommen, F. (eds) Advances in Analysis and Geometry. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7838-8_10
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DOI: https://doi.org/10.1007/978-3-0348-7838-8_10
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9589-7
Online ISBN: 978-3-0348-7838-8
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