Abstract
AbstractIn view of a better understanding of the geometry of scalar flat Kähler metrics, this paper studies two families of scalar flat Kähler metrics constructed by Hwang and Singer (Trans Am Math Soc 354(6):2285–2325, 2002) on $$\mathbb {C}^{n+1}$$
C
n
+
1
and on $${\mathcal {O}}(-k)$$
O
(
-
k
)
. For the metrics in both the families, we prove the existence of an asymptotic expansion for their $$\epsilon $$
ϵ
-functions and we show that they can be approximated by a sequence of projectively induced Kähler metrics. Further, we show that the metrics on $$\mathbb {C}^{n+1}$$
C
n
+
1
are not projectively induced, and that the Burns–Simanca metric is characterized among the scalar flat metrics on $${\mathcal {O}}(-k)$$
O
(
-
k
)
to be the only projectively induced one as well as the only one whose second coefficient in the asymptotic expansion of the $$\epsilon $$
ϵ
-function vanishes.
Funder
Università degli Studi di Parma
Publisher
Springer Science and Business Media LLC
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