Duke Mathematical Journal

Curvature and characteristic numbers of hyper-Kähler manifolds

Nigel Hitchin and Justin Sawon

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Characteristic numbers of compact hyper-Kähler manifolds are expressed in graph-theoretical form, considering them as a special case of the curvature invariants introduced by L. Rozansky and E. Witten. The appropriate graphs are generated by "wheels," and the recently proved Wheeling theorem is used to give a formula for the $\mathscr{L}$2-norm of the curvature of an irreducible hyper-Kähler manifold in terms of the volume and Pontryagin numbers. The formula involves the multiplicative sequence that is the square root of the Â-polynomial.

Article information

Duke Math. J., Volume 106, Number 3 (2001), 599-615.

First available in Project Euclid: 13 August 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C26: Hyper-Kähler and quaternionic Kähler geometry, "special" geometry
Secondary: 32J27: Compact Kähler manifolds: generalizations, classification 57M27: Invariants of knots and 3-manifolds 57R20: Characteristic classes and numbers


Hitchin, Nigel; Sawon, Justin. Curvature and characteristic numbers of hyper-Kähler manifolds. Duke Math. J. 106 (2001), no. 3, 599--615. doi:10.1215/S0012-7094-01-10637-6. https://projecteuclid.org/euclid.dmj/1092403944

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