ISSN:
1572-9060
Keywords:
conformal metrics
;
extremal Kähler metrics
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract On a compact complex manifold (M, J) of the Kähler type, we consider the functional defined by the L2-norm of the scalar curvature with its domain the space of Kähler metrics of fixed total volume. We calculate its critical points, and derive a formula that relates the Kähler and Ricci forms of such metrics on surfaces. If these metrics have a nonzero constant scalar curvature, then they must be Einstein. For surfaces, if the scalar curvature is nonconstant, these critical metrics are conformally equivalent to non-Kähler Einstein metrics on an open dense subset of the manifold. We also calculate the Hessian of the lower bound of the functional at a critical extremal class, and show that, in low dimensions, these classes are weakly stable minima for the said bound. We use this result to discuss some applications concerning the two-points blow-up of CP2.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1006688000057
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