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Annals of Global Analysis and Geometry

, Volume 43, Issue 4, pp 397–408 | Cite as

Canonical-type connection on almost contact manifolds with B-metric

  • Mancho ManevEmail author
  • Miroslava Ivanova
Article

Abstract

The canonical-type connection on the almost contact manifolds with B-metric is constructed. It is proved that its torsion is invariant with respect to a subgroup of the general conformal transformations of the almost contact B-metric structure. The basic classes of the considered manifolds are characterized in terms of the torsion of the canonical-type connection.

Keywords

Almost contact manifold B-metric Natural connection Canonical connection Conformal transformation Torsion tensor 

Mathematics Subject Classification (2000)

53C05 53C15 53C50 

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References

  1. 1.
    Blair D.E.: Riemannian Geometry of Contact and Symplectic Manifolds. Progress in Mathematics. Birkhäuser, Boston (2002)Google Scholar
  2. 2.
    Friedrich T., Ivanov S.: Parallel spinors and connections with skew-symmetric torsion in string theory. Asian J. Math. 6, 303–336 (2002)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Friedrich T., Ivanov S.: Almost contact manifolds, connections with torsion, and parallel spinors. J. Reine Angew. Math. 559, 217–236 (2003)MathSciNetzbMATHGoogle Scholar
  4. 4.
    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(56), 107–121 (1987)MathSciNetGoogle Scholar
  5. 5.
    Ganchev G., Ivanov S.: Characteristic curvatures on complex Riemannian manifolds. Riv. Mat. Univ. Parma (5) 1, 155–162 (1992)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Ganchev G., Mihova V.: Canonical connection and the canonical conformal group on an almost complex manifold with B-metric. Annuaire Univ. Sofia Fac. Math. Inform. 81, 195–206 (1987)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Ganchev G., Mihova V., Gribachev K.: Almost contact manifolds with B-metric. Math. Balkanica (N.S.) 7(3–4), 261–276 (1993)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Gates S.J., Hull C.M., Roček M.: Twisted multiplets and new supersymmetric non-linear σ-models. Nucl. Phys. B 248, 157–186 (1984)CrossRefGoogle Scholar
  9. 9.
    Gauduchon P.: Hermitian connections and Dirac operators. Boll. Unione Mat. Ital. 11, 257–288 (1997)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Gribacheva D.: Natural connections on Riemannian product manifolds. C. R. Acad. Bulgare Sci. 64(6), 799–806 (2011)MathSciNetGoogle Scholar
  11. 11.
    Gribacheva D.: Natural connections on conformal Riemannian P-manifolds. C. R. Acad. Bulgare Sci. 65(5), 581–590 (2012)zbMATHGoogle Scholar
  12. 12.
    Gribacheva D., Mekerov D.: Canonical connection on a class of Riemannian almost product manifolds. J. Geom. 102(1–2), 53–71 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Hayden H.: Subspaces of a space with torsion. Proc. London Math. Soc. 34, 27–50 (1934)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Ivanov S., Papadopoulos G.: Vanishing theorems and string backgrounds. Classical Quantum Gravity 18, 1089–1110 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Lichnerowicz A.: Un théorème sur les espaces homogènes complexes. Arch. Math. 5, 207–215 (1954)MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Lichnerowicz A.: Généralisation de la géométrie kählérienne globale. Colloque de Géométrie Différentielle, Louvain 16, 99–122 (1955)Google Scholar
  17. 17.
    Manev, M.: Properties of curvature tensors on almost contact manifolds with B-metric. In: Proceedings of Jubilee Scientific Session of Vassil Levsky Higher Military School, Veliko Tarnovo, vol. 27, pp. 221–227 (1993)Google Scholar
  18. 18.
    Manev M.: Contactly conformal transformations of general type of almost contact manifolds with B-metric. Appl. Math. Balkanica (N.S.) 11(3–4), 347–357 (1997)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Manev M.: A connection with totally skew-symmetric torsion on almost contact manifolds with B-metric. Internat. J. Geom. Methods Mod. Phys. 9(5), 1250044 (2012)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Manev M., Gribachev K.: Contactly conformal transformations of almost contact manifolds with B-metric. Serdica Math. J. 19, 287–299 (1993)MathSciNetzbMATHGoogle Scholar
  21. 21.
    Manev M., Gribachev K.: Conformally invariant tensors on almost contact manifolds with B-metric. Serdica Math. J. 20, 133–147 (1994)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Manev, M., Ivanova, M.: A classification of the torsion tensors on almost contact manifolds with B-metric. arXiv:1105.5715Google Scholar
  23. 23.
    Manev M., Ivanova M.: A natural connection on some classes of almost contact manifolds with B-metric. C. R. Acad. Bulgare Sci. 65(4), 429–436 (2012)MathSciNetGoogle Scholar
  24. 24.
    Mekerov D.: Canonical connection on quasi-Kähler manifolds with Norden metric. J. Tech. Univ. Plovdiv Fundam. Sci. Appl. Ser. A Pure Appl. Math. 14, 73–86 (2009)Google Scholar
  25. 25.
    Sasaki S., Hatakeyama Y.: On differentiable manifolds with certain structures which are closely related to almost contact structures II. Tôhoku Math. J. 13, 281–294 (1961)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Strominger A.: Superstrings with torsion. Nucl. Phys. B 274, 253–284 (1986)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Algebra and Geometry, Faculty of Mathematics and InformaticsUniversity of PlovdivPlovdivBulgaria

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