Curvature and Characteristic Numbers of Hyper-kähler Manifolds

  title={Curvature and Characteristic Numbers of Hyper-k{\"a}hler Manifolds},
  author={Nigel J. Hitchin and Justin Sawon},
Characteristic numbers of compact hyper-Kähler manifolds are expressed in graphtheoretical 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 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… CONTINUE READING
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