Duke Mathematical Journal

A Burns-Epstein invariant for ACHE 4-manifolds

Olivier Biquard and Marc Herzlich

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We define a renormalized characteristic class for Einstein asymptotically complex hyperbolic (ACHE) manifolds of dimension 4: for any such manifold, the polynomial in the curvature associated to the characteristic class χ−3τ is shown to converge. This extends a work of Burns and Epstein in the Kähler-Einstein case

We also define a new global invariant for any compact 3-dimensional strictly pseudoconvex Cauchy-Riemann (CR) manifold by a renormalization procedure of the η-invariant of a sequence of metrics that approximate the CR structure.

Finally, we get a formula relating the renormalized characteristic class to the topological number χ−3τ and the invariant of the CR structure arising at infinity.

Article information

Duke Math. J. Volume 126, Number 1 (2005), 53-100.

First available in Project Euclid: 15 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C55: Hermitian and Kählerian manifolds [See also 32Cxx] 58J37: Perturbations; asymptotics 58J60: Relations with special manifold structures (Riemannian, Finsler, etc.)
Secondary: 32V15: CR manifolds as boundaries of domains 58J28: Eta-invariants, Chern-Simons invariants


Biquard, Olivier; Herzlich, Marc. A Burns-Epstein invariant for ACHE 4-manifolds. Duke Math. J. 126 (2005), no. 1, 53--100. doi:10.1215/S0012-7094-04-12612-0. http://projecteuclid.org/euclid.dmj/1103136475.

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