A A Malykh et al 2003 Class. Quantum Grav. 20 L263 doi:10.1088/0264-9381/20/22/L01
Anti-self-dual Riemannian metrics without Killing vectors: can they be realized on K3?
FREE ARTICLEA A Malykh1, Y Nutku2 and M B Sheftel1,2
Show affiliationsLETTER TO THE EDITOR
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 homogeneous 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.
- PACS
-
02.40.Ky Riemannian geometries
- MSC
-
14J28 K3 surfaces and Enriques surfaces
53B20 Local Riemannian geometry
51M05 Euclidean geometries (general) and generalizations
83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
- Subjects
- Dates
-
Issue 22 (21 November 2003)
Received 3 March 2003
Published 6 October 2003
-
Anti-self-dual Riemannian metrics without Killing vectors: can they be realized on K3?
A A Malykh et al 2003 Class. Quantum Grav. 20 L263
-
Turbulent flows at cryogenic temperatures: a new frontier
L Skrbek et al 1999 J. Phys.: Condens. Matter 11 7761
-
The HELLAS2XMM Survey. VII. The Hard X-Ray Luminosity Function of AGNs up to z = 4: More Absorbed AGNs at Low Luminosities and High Redshifts
F. La Franca et al. 2005 ApJ 635 864
-
Unpulsed Optical Emission from the Crab Pulsar
A. Golden et al. 2000 ApJ 535 373
-
Finite-temperature correlations for the Uq(
(2|1))-invariant generalized Hubbard model
Kazumitsu Sakai and Andreas Klümper 2001 J. Phys. A: Math. Gen. 34 8015
-
Nonholonomic left and right flows on Lie groups
Bozidar Jovanovic 1999 J. Phys. A: Math. Gen. 32 8293
-
Density Fluctuations in MHD Turbulence: Spectra, Intermittency, and Topology
G. Kowal et al. 2007 ApJ 658 423
-
pp-waves with torsion and metric-affine gravity
Vedad Pasic and Dmitri Vassiliev 2005 Class. Quantum Grav. 22 3961
-
Asymptotically flat soliton solutions in bosonic string theory
Oleg V Kechkin 2003 Class. Quantum Grav. 20 L225
-
Induced voltage of piezoelectric unimorph cantilevers of different nonpiezoelectric/piezoelectric length ratios
Xiaotong Gao et al 2009 Smart Mater. Struct. 18 125018
Related review articles
What's this?- Loop quantum cosmology: a status report
- Tunnelling methods and Hawking's radiation: achievements and prospects
- Quantitative approaches to information recovery from black holes