Almost Contact B-metric Manifoldsas Extensions of a 2-dimensional Space-form

Hristo M. Manev

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2016)

  • Volume: 55, Issue: 1, page 59-71
  • ISSN: 0231-9721

Abstract

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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.

How to cite

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Manev, Hristo M.. "Almost Contact B-metric Manifoldsas Extensions of a 2-dimensional Space-form." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 55.1 (2016): 59-71. <http://eudml.org/doc/286712>.

@article{Manev2016,
abstract = {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.},
author = {Manev, Hristo M.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Almost contact manifold; B-metric; cone; $S^1$-solvable extension; complex space-form; Norden metric},
language = {eng},
number = {1},
pages = {59-71},
publisher = {Palacký University Olomouc},
title = {Almost Contact B-metric Manifoldsas Extensions of a 2-dimensional Space-form},
url = {http://eudml.org/doc/286712},
volume = {55},
year = {2016},
}

TY - JOUR
AU - Manev, Hristo M.
TI - Almost Contact B-metric Manifoldsas Extensions of a 2-dimensional Space-form
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2016
PB - Palacký University Olomouc
VL - 55
IS - 1
SP - 59
EP - 71
AB - 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.
LA - eng
KW - Almost contact manifold; B-metric; cone; $S^1$-solvable extension; complex space-form; Norden metric
UR - http://eudml.org/doc/286712
ER -

References

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  1. Blair, D. E., Riemannian Geometry of Contact and Symplectic Manifolds, . Progress in Mathematics 203, Birkhäuser, Boston, 2002. (2002) Zbl1011.53001MR1874240
  2. Ganchev, G., Borisov, A., Note on the almost complex manifolds with a Norden metric, . C. R. Acad. Bulg. Sci. 39 (1986), 31–34. (1986) Zbl0608.53031MR0857345
  3. Ganchev, G., Mihova, V., Gribachev, K., Almost contact manifolds with B-metric, . Math. Balkanica (N.S.) 7 (1993), 261–276. (1993) Zbl0830.53031MR1269881
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  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. (2015) MR3519740
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  13. Manev, M., Gribachev, K., Conformally invariant tensors on almost contact manifolds with B-metric, . Serdica Math. J. 20 (1994), 133–147. (1994) Zbl0833.53034MR1333343
  14. Manev, M., Ivanova, M., 10.1007/s10455-012-9351-z, . Ann. Global Anal. Geom. 43, 4 (2013), 397–408. (2013) MR3038542DOI10.1007/s10455-012-9351-z
  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. (2014) Zbl1310.53069MR3224009
  16. Mekerov, D., Manev, M., On the geometry of quasi-Kähler manifolds with Norden metric, . Nihonkai Math. J. 16 (2005), 89–93. (2005) Zbl1094.53021MR2217549
  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. (1997) Zbl1032.53022MR1657412

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