Podrobný výpis o publikaci

FERRAIOLI, Diego Catalano a Michal MARVAN. The equivalence problem for generic four-dimensional metrics with two commuting Killing vectors. Annali di Matematica Pura ed Applicata. HEIDELBERG: SPRINGER HEIDELBERG, 2020, roč. 199, č. 4, s. 1343-1380. ISSN 0373-3114. doi:10.1007/s10231-019-00924-y.
Další formáty: BibTeX LaTeX RIS @article{49242, author = {Ferraioli, Diego Catalano and Marvan, Michal}, article_location = {HEIDELBERG}, article_number = {4}, doi = {http://dx.doi.org/10.1007/s10231-019-00924-y}, keywords = {Differential invariants; Metric equivalence problem; Kundu class}, language = {eng}, issn = {0373-3114}, journal = {Annali di Matematica Pura ed Applicata}, title = {The equivalence problem for generic four-dimensional metrics with two commuting Killing vectors}, url = {https://link.springer.com/article/10.1007/s10231-019-00924-y}, volume = {199}, year = {2020} } TY - JOUR ID - 49242 AU - Ferraioli, Diego Catalano - Marvan, Michal PY - 2020 TI - The equivalence problem for generic four-dimensional metrics with two commuting Killing vectors JF - Annali di Matematica Pura ed Applicata VL - 199 IS - 4 SP - 1343-1380 EP - 1343-1380 PB - SPRINGER HEIDELBERG SN - 03733114 KW - Differential invariants KW - Metric equivalence problem KW - Kundu class UR - https://link.springer.com/article/10.1007/s10231-019-00924-y N2 - We consider the equivalence problem of four-dimensional semi-Riemannian metrics with the two-dimensional Abelian Killing algebra. In the generic case we determine a semi-invariant frame and a fundamental set of first-order 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 non-integrable), 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 non-generic cases, we also find all Lambda-vacuum 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 Lambda-vacuum 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 a Michal MARVAN. The equivalence problem for generic four-dimensional metrics with two commuting Killing vectors. \textit{Annali di Matematica Pura ed Applicata}. HEIDELBERG: SPRINGER HEIDELBERG, 2020, roč.~199, č.~4, s.~1343-1380. ISSN~0373-3114. doi:10.1007/s10231-019-00924-y.

FERRAIOLI, Diego Catalano a Michal MARVAN. The equivalence problem for generic four-dimensional metrics with two commuting Killing vectors. Annali di Matematica Pura ed Applicata. HEIDELBERG: SPRINGER HEIDELBERG, 2020, roč. 199, č. 4, s. 1343-1380. ISSN 0373-3114. doi:10.1007/s10231-019-00924-y.

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Základní údaje
Originální název	The equivalence problem for generic four-dimensional metrics with two commuting Killing vectors
Autoři	FERRAIOLI, Diego Catalano (380 Itálie) a Michal MARVAN (203 Česká republika, domácí).
Vydání	Annali di Matematica Pura ed Applicata, HEIDELBERG, SPRINGER HEIDELBERG, 2020, 0373-3114.

Další údaje
Originální jazyk	angličtina
Typ výsledku	Článek v odborném periodiku
Obor	10101 Pure mathematics
Stát vydavatele	Německo
Utajení	není předmětem státního či obchodního tajemství
WWW	Annali di Matematica Pura ed Applicata
Kód RIV	RIV/47813059:19610/20:A0000066
Organizační jednotka	Matematický ústav v Opavě
Doi	http://dx.doi.org/10.1007/s10231-019-00924-y
UT WoS	000494394800001
Klíčová slova anglicky	Differential invariants; Metric equivalence problem; Kundu class
Štítky	MÚ
Příznaky	Mezinárodní význam, Recenzováno
Návaznosti	GBP201/12/G028, projekt VaV.
Změnil	Změnil: Mgr. Aleš Ryšavý, učo 28000. Změněno: 19. 3. 2021 12:29.

Anotace
We consider the equivalence problem of four-dimensional semi-Riemannian metrics with the two-dimensional Abelian Killing algebra. In the generic case we determine a semi-invariant frame and a fundamental set of first-order 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 non-integrable), 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 non-generic cases, we also find all Lambda-vacuum 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 Lambda-vacuum 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.

Anotace

We consider the equivalence problem of four-dimensional semi-Riemannian metrics with the two-dimensional Abelian Killing algebra. In the generic case we determine a semi-invariant frame and a fundamental set of first-order 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 non-integrable), 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 non-generic cases, we also find all Lambda-vacuum 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 Lambda-vacuum 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.