Matrix Lie Groups as 3-Dimensional Almost Contact B-Metric Manifolds
Abstract
The object of investigation are Lie groups considered as almost contact B-metric manifolds of the lowest dimension three. It is established a correspondence of all basic-class-manifolds of the Ganchev-Mihova-Gribachev classification of the studied manifolds and the explicit matrix representation of Lie groups. Some known Lie groups are equipped with almost contact B-metric structure of different types.
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bibitem{Bia1}
{sc L. Bianchi}: textit{Sugli spazi a tre dimensioni che ammettono un gruppo
continuo di movimenti}.
Memorie di Matematica e di Fisica della Societa
Italiana delle Scienze, Serie Terza {bf 11} (1898), 267--352.
bibitem{Bia2}
{sc L. Bianchi}: textit{On the three-dimensional spaces which admit a continuous group of motions}.
Gen. Rel. Grav. {bf 33} (2001), 2171--2253.
bibitem{Blair}
{sc D. E. Blair}: textit{Riemannian Geometry of Contact and Symplectic
Manifolds}. Progress in Mathematics, Birkhauser, Boston, 2002.
bibitem{GaBo}
{sc G. Ganchev {rm and} A. Borisov}: textit{Note on the almost complex
manifolds with a Norden metric}. C. R. Acad. Bulg. Sci. {bf 39} (1986), 31--34.
bibitem{GaMiGr}
{sc G. Ganchev, V. Mihova {rm and} K. Gribachev}: textit{Almost contact
manifolds with B-metric}. Math. Balkanica (N.S.) {bf 7} (1993), 261--276.
bibitem{Gil}
{sc R. Gilmore}: textit{Lie Groups, Lie Algebras and Some of Their Applications}.
John Wiley & Sons, Inc., New York, 1974.
bibitem{GrMeDj}
{sc K. Gribachev, D. Mekerov {rm and} G. Djelepov}: textit{Generalized
B-manifolds}. C. R. Acad. Bulg. Sci. {bf 38} (1985), 299--302.
bibitem{Kow}
{sc O. Kowalski}: textit{
Generalized Symmetric Spaces}. Lecture Notes in Mathematics, 805 (A. Dold, B. Eckmann, eds.), Springer, Heidelberg, 1980.
bibitem{HM}
{sc H. Manev}: textit{On the structure tensors of almost contact
B-metric manifolds}. arXiv:allowbreak{}1405.3088.
bibitem{HM-Bia}
{sc H. Manev}: textit{Almost contact B-metric structures and the Bianchi classification of the three-dimensional Lie algebras}. arXiv:allowbreak{}1412.8142.
bibitem{IcoMek}
{sc H. Manev {rm and} D. Mekerov}: textit{Lie groups as 3-dimensional almost contact B-metric manifolds}.
J. Geom., Online September 2014, DOI:10.1007/s00022-014-0244-0.
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