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Anti-self-dual Riemannian metrics without Killing vectors, can they be realized on K3? | | A. A. Malykh
; Y. Nutku
; M. B. Sheftel
; | | Date: |
18 Apr 2003 | | Subject: | gr-qc hep-th | | Abstract: | Explicit Riemannian metrics with Euclidean signature and anti-self dual curvature that do not admit any Killing vectors are presented. The metric and the Riemann curvature scalars are homogenous functions of degree zero in a single real potential and its derivatives. The solution for the potential is a sum of exponential functions which suggests that for the choice of a suitable domain of coordinates and parameters it can be the metric on a compact manifold. Then, by the theorem of Hitchin, it could be a class of metrics on $K3$, or on surfaces whose universal covering is $K3$. | | Source: | arXiv, gr-qc/0304066 | | Services: | Forum | Review | PDF | Favorites | |
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