Mathematics
The eta invariant in the doubly Kählerian conformally compact Einstein case
Document Type
Article
Abstract
On a 3-manifold bounding a compact 4-manifold, 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 Kähler-Ricci 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 Duistermaat-Heckman theorem. This result is closely related to earlier work of Hitchin on the Einstein selfdual case. © 2011 Springer-Verlag.
Publication Title
Mathematische Zeitschrift
Publication Date
8-2012
Volume
271
Issue
3-4
First Page
1065
Last Page
1073
ISSN
0025-5874
DOI
10.1007/s00209-011-0903-x
Keywords
conformally compact, Duistermmat-Heckman Theorem, Einstein metric, Eta invariant, Kahler metric
Repository Citation
Maschler, Gideon, "The eta invariant in the doubly Kählerian conformally compact Einstein case" (2012). Mathematics. 35.
https://commons.clarku.edu/mathematics/35
