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@article{49242, author = {Ferraioli, Diego Catalano and Marvan, Michal}, article_location = {HEIDELBERG}, article_number = {4}, doi = {http://dx.doi.org/10.1007/s1023101900924y}, keywords = {Differential invariants; Metric equivalence problem; Kundu class}, language = {eng}, issn = {03733114}, journal = {Annali di Matematica Pura ed Applicata}, title = {The equivalence problem for generic fourdimensional metrics with two commuting Killing vectors}, url = {https://link.springer.com/article/10.1007/s1023101900924y}, volume = {199}, year = {2020} }
TY  JOUR ID  49242 AU  Ferraioli, Diego Catalano  Marvan, Michal PY  2020 TI  The equivalence problem for generic fourdimensional metrics with two commuting Killing vectors JF  Annali di Matematica Pura ed Applicata VL  199 IS  4 SP  13431380 EP  13431380 PB  SPRINGER HEIDELBERG SN  03733114 KW  Differential invariants KW  Metric equivalence problem KW  Kundu class UR  https://link.springer.com/article/10.1007/s1023101900924y N2  We consider the equivalence problem of fourdimensional semiRiemannian metrics with the twodimensional Abelian Killing algebra. In the generic case we determine a semiinvariant frame and a fundamental set of firstorder scalar differential invariants suitable for solution of the equivalence problem. Genericity means that the Killing leaves are not null, the metric is not orthogonally transitive (i.e., the distribution orthogonal to the Killing leaves is nonintegrable), and two explicitly constructed scalar invariants C rho and lC are nonzero. All the invariants are designed to have tractable coordinate expressions. Assuming the existence of two functionally independent invariants, we solve the equivalence problem in two ways. As an example, we invariantly characterize the Van den Bergh metric. To understand the nongeneric cases, we also find all Lambdavacuum metrics that are generic in the above sense, except that either C rho or lC is zero. In this way we extend the Kundu class to Lambdavacuum metrics. The results of the paper can be exploited for invariant characterization of classes of metrics and for extension of the set of known solutions of the Einstein equations. ER 
FERRAIOLI, Diego Catalano and Michal MARVAN. The equivalence problem for generic fourdimensional metrics with two commuting Killing vectors. \textit{Annali di Matematica Pura ed Applicata}. HEIDELBERG: SPRINGER HEIDELBERG, 2020, vol.~199, No~4, p.~13431380. ISSN~03733114. doi:10.1007/s1023101900924y.
