NDLI: Strongly Extremal Kähler Metrics

Content Provider	Springer Nature Link
Author	Simanca, Santiago R.
Copyright Year	2000
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.
Starting Page	29
Ending Page	46
Page Count	18
File Format	PDF
ISSN	0232704X
Journal	Annals of Global Analysis and Geometry
Volume Number	18
Issue Number	1
e-ISSN	15729060
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2000-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Group Theory and Generalizations Analysis Geometry Mathematical and Computational Physics Statistics for Business/Economics/Mathematical Finance/Insurance
Content Type	Text
Resource Type	Article
Subject	Analysis Geometry and Topology

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