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Title of Journal: Math Z

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Abbravation: Mathematische Zeitschrift

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Springer-Verlag

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DOI

10.1016/0006-2952(91)90642-i

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1432-1823

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The eta invariant in the doubly Kählerian conforma

Authors: Gideon Maschler
Publish Date: 2011/07/08
Volume: 271, Issue: 3-4, Pages: 1065-1073
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Abstract

On a 3manifold bounding a compact 4manifold let a conformal structure be induced from a complete Einstein metric which conformally compactifies to a Kähler metric Formulas are derived for the eta invariant of this conformal structure under additional assumptions One such assumption is that the Kähler metric admits a special KählerRicci potential in the sense defined by Derdzinski and Maschler Another is that the Kähler metric is part of an ambitoric structure in the sense defined by Apostolov Calderbank and Gauduchon as well as a toric one The formulas are derived using the DuistermaatHeckman theorem This result is closely related to earlier work of Hitchin on the Einstein selfdual case

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