We propose two conjectures about Ricci-flat Kähler metrics: Conjecture 1: A Ricci-flat projectively induced metric is flat. Conjecture 2: A Ricci-flat metric on an n-dimensional complex manifold such that the an+1 coefficient of the TYZ expansion vanishes is flat. We verify Conjecture 1 (see Theorem 1.1) under the assumptions that the metric is radial and stable-projectively induced and Conjecture 2 (see Theorem 1.2) for complex surfaces whose metric is either radial or complete and ALE. We end the paper by showing, by means of the Simanca metric, that the assumption of Ricci-flatness in Conjecture 1 and in Theorem 1.2 cannot be weakened to scalar-flatness (see Theorem 1.3).
Two conjectures on Ricci-flat Kähler metrics / Loi, Andrea; Salis, Filippo; Zuddas, Fabio. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - 290(2018), pp. 599-613.
Titolo: | Two conjectures on Ricci-flat Kähler metrics |
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Data di pubblicazione: | 2018 |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00209-017-2033-6 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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http://hdl.handle.net/11583/2707519