Geometric characteristics and properties of a two-parametric family of Lie groups with almost contact B-metric structure of the smallest dimension

Miroslava Ivanova, Lilko Dospatliev

Abstract


Almost contact B-metric manifolds of the lowest dimension 3 are constructed by a two-parametric family of Lie groups. The our purpose is to determine the class of considered manifolds in a classication of almost contact B-metric manifolds and theirs the most important geometric characteristics and properties.


Keywords


almost contact B-metric manifold, Lie group, Lie algebra, indenite metric

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References


Ganchev, G., Mihova, V., Gribachev, K., Almost contact manifolds with B-metric, Math. Balkanica (N.S.), 7(1993), 261-276.

Ganchev, G., Borisov A., Note on the almost complex manifolds with a Norden metric, C. R. Acad. Bulg. Sci., 39(1986), 31-34.

Gribachev, K., Mekerov, D., Djelepov, G., Generalized B-manifolds, C. R. Acad. Bulg. Sci., 38(1985), 299-302.

Manev, M., Contactly conformal transformations of general type of almost contact manifolds with B-metric Applications, Math. Balkanica (N.S.), 11(1997), 347-357.

Manev, M., Natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric, Int. J. Geom. Methods Mod. Phys., 9(2012), no. 5, 20 pages.

Manev, M., Gribachev, K., Contactlly conformal transformations of almost contact manifolds with B-metric, Serdica Math. J., 19(1993), 287-299.

Manev, M., Gribachev, K., Conformally invariant tensors on almost contact manifolds with B-metric, Serdica Math. J., 20(1994), 133-147.

Manev, M., Ivanova, M., Canonical-type connection on almost contact manifolds with B-metric, Ann. Global Anal. Geom., 43(2013), no. 4, 397-408.

Manev, M., Ivanova, M., A classication of the torsions on almost contact manifolds with B-metric, Cent. Eur. J. Math., 12(2014), no. 10, 1416-1432.

Nakova, G., Gribachev, K. Submanifolds of some almost contact manifolds with

B-metric with codimension two, I. Math. Balkanica (N.S.), 12(1998), no. 1-2, 93-108.

Manev, H., Mekerov, D., Lie groups as 3-dimentional almost B-metric manifolds, J. Geom., 106(2015), no. 2, 229-242.

Ivanov, S., Manev, H., Manev, M., Sasaki-like almost contact complex Riemannian manifolds, J. Geom. Phys., 107(2016), 136-148.

Manev, M., Curvature properties on some classes of almost contact manifolds with B-mertic, C. R. Acad. Bulg. Sci., 65(2012), no. 3, 283-290.

Manev, M., Ivanova, M., A natural connection on some classes of almost contact manifolds with B-metric, C. R. Acad. Bulg. Sci., 65(2012), no. 4, 429-436.

Manev, M., Properties of curvature tensors on almost contact manifolds with

B-metric, Proc. of Jubilee Sci. Session of Vasil Levski Higher Mil. School, Veliko

Tarnovo, 27(1993), 221-227.

Ganchev, G., Gribachev, K., Mihova, V., B-connections and their conformal

invariants on conformally Kaehler manifolds with B-metric, Publ. Inst. Math.,

Beograd (N.S.), 42(1987), no. 56, 107-121.

Manev, H., On the structure tensors of almost contact B-metric manifolds,

Filomat, 29(2015), no. 3, 427-436.

Manev, H., Almost contact B-metric structures and the Bianchi classication

of the three-dimensional Lie algebras, arXiv:1412.8142.

Bianchi, L., Sugli spazi a tre dimensioni che ammettono un gruppo continuo

di movimenti, Memorie di Matematica e di Fisica della Societa Italiana della Scienze, Serie Terza, 11(1898), 267-352.

Bianchi, L., On the three-dimensional spaces which admit a continuous group

of motions, Gen. Rel. Grav., 33(2001), 2171-2253.




DOI: http://dx.doi.org/10.24193/subbmath.2019.4.12

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