JOURNAL OF GEOMETRY AND PHYSICS | 卷:70 |
Extremal Kahler metrics and Bach-Merkulov equations | |
Article | |
Koca, Caner | |
关键词: Einstein metrics; Extremal Miller metrics; Bach tensor; Weyl curvature; Einstein-Maxwell equations; | |
DOI : 10.1016/j.geomphys.2013.03.025 | |
来源: Elsevier | |
【 摘 要 】
In this paper, we study a coupled system of equations on oriented compact 4-manifolds which we call the Bach-Merkulov equations. These equations can be thought of as the conformally invariant version of the classical Einstein-Maxwell equations. Inspired by the work of C. LeBrun on Einstein-Maxwell equations on compact Kahler surfaces, we give a variational characterization of solutions to Bach-Merkulov equations as critical points of the Weyl functional. We also show that extremal Kahler metrics are solutions to these equations, although, contrary to the Einstein-Maxwell analogue, they are not necessarily minimizers of the Weyl functional. We illustrate this phenomenon by studying the Calabi action on Hirzebruch surfaces. (C) 2013 Elsevier B.V. All rights reserved.
【 授权许可】
Free
【 预 览 】
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