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- Title
Quarter-pinched Einstein metrics interpolating between real and complex hyperbolic metrics.
- Authors
Cortés, V.; Saha, A.
- Abstract
We show that the one-loop quantum deformation of the universal hypermultiplet provides a family of complete 1 / 4-pinched negatively curved quaternionic Kähler (i.e. half conformally flat Einstein) metrics gc<inline-graphic></inline-graphic>, c≥0<inline-graphic></inline-graphic>, on R4<inline-graphic></inline-graphic>. The metric g0<inline-graphic></inline-graphic> is the complex hyperbolic metric whereas the family (gc)c>0<inline-graphic></inline-graphic> is equivalent to a family of metrics (hb)b>0<inline-graphic></inline-graphic> depending on b=1/c<inline-graphic></inline-graphic> and smoothly extending to b=0<inline-graphic></inline-graphic> for which h0<inline-graphic></inline-graphic> is the real hyperbolic metric. In this sense the one-loop deformation interpolates between the real and the complex hyperbolic metrics. We also determine the (singular) conformal structure at infinity for the above families.
- Publication
Mathematische Zeitschrift, 2018, Vol 290, Issue 1/2, p155
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-017-2013-x