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 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

 Fundam. Prikl. Mat., 2015, Volume 20, Issue 3, Pages 257–271 (Mi fpm1662)

Isometry groups of $4$-dimensional nilpotent Lie groups

T. Šukilović

Abstract: The main purpose of this paper is to give a complete description of isometry groups on the $4$-dimensional simply connected nilpotent Lie groups. We distinguish between two geometrically distinct cases of degenerate and nondegenerate center of the group. Since Walker metrics appear as the underlying structure of neutral signature metrics on the nilpotent Lie groups with degenerate center, we find necessary and sufficient condition for them to locally admit the nilpotent group of isometries.

 Funding Agency Grant Number Ministry of Education, Science and Technical Development of Serbia 174012

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English version:
Journal of Mathematical Sciences (New York), 2017, 225:4, 711–721

Bibliographic databases:

UDC: 512.813

Citation: T. Šukilović, “Isometry groups of $4$-dimensional nilpotent Lie groups”, Fundam. Prikl. Mat., 20:3 (2015), 257–271; J. Math. Sci., 225:4 (2017), 711–721

Citation in format AMSBIB
\Bibitem{Suk15} \by T.~{\v S}ukilovi\'c \paper Isometry groups of $4$-dimensional nilpotent Lie groups \jour Fundam. Prikl. Mat. \yr 2015 \vol 20 \issue 3 \pages 257--271 \mathnet{http://mi.mathnet.ru/fpm1662} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3519757} \elib{http://elibrary.ru/item.asp?id=31996137} \transl \jour J. Math. Sci. \yr 2017 \vol 225 \issue 4 \pages 711--721 \crossref{https://doi.org/10.1007/s10958-017-3488-z}