| Title:
|
Almost Contact B-metric Manifoldsas Extensions of a 2-dimensional Space-form (English) |
| Author:
|
Manev, Hristo M. |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
59-71 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The object of investigations are almost contact B-metric manifolds which are derived as a product of a real line and a 2-dimensional manifold equipped with a complex structure and a Norden metric. There are used two different methods for generation of the B-metric on the product manifold. The constructed manifolds are characterised with respect to the Ganchev–Mihova–Gribachev classification and their basic curvature properties. (English) |
| Keyword:
|
Almost contact manifold |
| Keyword:
|
B-metric |
| Keyword:
|
cone |
| Keyword:
|
$S^1$-solvable extension |
| Keyword:
|
complex space-form |
| Keyword:
|
Norden metric |
| MSC:
|
53C15 |
| MSC:
|
53C50 |
| idZBL:
|
Zbl 1365.53035 |
| idMR:
|
MR3674601 |
| . |
| Date available:
|
2016-08-30T11:56:24Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145818 |
| . |
| Reference:
|
[1] Blair, D. E.: Riemannian Geometry of Contact and Symplectic Manifolds.. Progress in Mathematics 203, Birkhäuser, Boston, 2002. Zbl 1011.53001, MR 1874240 |
| Reference:
|
[2] Ganchev, G., Borisov, A.: Note on the almost complex manifolds with a Norden metric.. C. R. Acad. Bulg. Sci. 39 (1986), 31–34. Zbl 0608.53031, MR 0857345 |
| Reference:
|
[3] Ganchev, G., Mihova, V., Gribachev, K.: Almost contact manifolds with B-metric.. Math. Balkanica (N.S.) 7 (1993), 261–276. Zbl 0830.53031, MR 1269881 |
| Reference:
|
[4] Gribachev, K., Mekerov, D., Djelepov, G.: Generalized B-manifolds.. C. R. Acad. Bulg. Sci. 38 (1985), 299–302. MR 0788392 |
| Reference:
|
[5] Ivanov, S., Manev, H., Manev, M.: Sasaki-like almost contact complex Riemannian manifolds.. arXiv.org arXiv:1402.5426 (2014), 1–19. MR 3521472 |
| Reference:
|
[6] Manev, H.: On the structure tensors of almost contact B-metric manifolds.. Filomat 29 (2015), 427–436. MR 3359436, 10.2298/FIL1503427M |
| Reference:
|
[7] Manev, H.: Almost contact B-metric structures and the Bianchi classification of the three-dimensional Lie algebras.. arXiv.org arXiv:1412.8142 (2014), 1–12. MR 3467741 |
| Reference:
|
[8] Manev, H.: Matrix Lie groups as 3-dimensional almost contact B-metric manifolds.. Facta Universitatis (Niš), Ser. Math. Inform 30, 3 (2015), 341–351, arXiv:1503.00312. MR 3352468 |
| Reference:
|
[9] Manev, H.: Space-like and time-like hyperspheres in real pseudo-Riemannian 4-spaces with almost contact B-metric structures.. arXiv.org arXiv:1504.00267 (2015), 1–8. MR 3519740 |
| Reference:
|
[10] Manev, H., Mekerov, D.: Lie groups as 3-dimensional almost contact B-metric manifolds.. J. Geom. 106 (2015), 229–242. Zbl 1327.53030, MR 3353833, 10.1007/s00022-014-0244-0 |
| Reference:
|
[11] Manev, M.: Natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric.. Int. J. Geom. Methods Mod. Phys. 9, 1250044 (2012), 1–20. Zbl 1261.53025, MR 2948863, 10.1142/S0219887812500442 |
| Reference:
|
[12] Manev, M., Gribachev, K.: Contactly conformal transformations on almost contact manifolds with B-metric.. Serdica Math. J. 19 (1993), 287–299. MR 1269769 |
| Reference:
|
[13] Manev, M., Gribachev, K.: Conformally invariant tensors on almost contact manifolds with B-metric.. Serdica Math. J. 20 (1994), 133–147. Zbl 0833.53034, MR 1333343 |
| Reference:
|
[14] Manev, M., Ivanova, M.: Canonical type connections on almost contact manifold with B-matric.. Ann. Global Anal. Geom. 43, 4 (2013), 397–408. MR 3038542, 10.1007/s10455-012-9351-z |
| Reference:
|
[15] Manev, M., Ivanova, M.: A classification of the torsion tensors on almost contact manifolds with B-metric.. Cent. Eur. J. Math. 12 (2014), 1416–1432. Zbl 1310.53069, MR 3224009 |
| Reference:
|
[16] Mekerov, D., Manev, M.: On the geometry of quasi-Kähler manifolds with Norden metric.. Nihonkai Math. J. 16 (2005), 89–93. Zbl 1094.53021, MR 2217549 |
| Reference:
|
[17] Nakova, G., Gribachev, K.: Submanifolds of some almost contact manifolds with B-metric with codimension two, I.. Math. Balkanica (N.S.) 11 (1997), 255–267. Zbl 1032.53022, MR 1657412 |
| . |
