Periodica Mathematica Hungarica

, Volume 77, Issue 1, pp 69–76 | Cite as

On structure-preserving connections

  • Arif SalimovEmail author


In this paper we find the formula of connections under which an almost complex structure is covariantly constant. These types of connections on anti-Kähler–Codazzi manifolds are described. Also, twin metric-preserving connections are analyzed for quasi-Kähler manifolds. Finally, anti-Hermitian Chern connections are investigated.


Almost complex structure Semi-Riemannian metric Anti-Hermitian structure Anti-Kähler–Codazzi manifold Anti-Kähler manifold Quasi-Kähler manifold Chern connection 

Mathematics Subject Classification

53C15 53C05 


  1. 1.
    C.-L. Bejan, M. Crasmareanu, Conjugate connections with respect to a quadratic endomorphism and duality. Filomat 30(9), 2367–2374 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    A.M. Blaga, M. Crasmareanu, The geometry of complex conjugate connections. Hacet. J. Math. Stat. 41(1), 119–126 (2012)MathSciNetzbMATHGoogle Scholar
  3. 3.
    A.M. Blaga, M. Crasmareanu, The geometry of product conjugate connections. An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 59(1), 73–84 (2013)MathSciNetzbMATHGoogle Scholar
  4. 4.
    A.M. Blaga, M. Crasmareanu, The geometry of tangent conjugate connections. Hacet. J. Math. Stat. 44(4), 767–774 (2015)MathSciNetzbMATHGoogle Scholar
  5. 5.
    S.S. Chern, Characteristic classes of Hermitian manifolds. Ann. Math. 47, 85–121 (1946)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    V. Cruceanu, Almost product bicomplex structures on manifolds. An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 51(1), 99–118 (2005)MathSciNetzbMATHGoogle Scholar
  7. 7.
    G.T. Ganchev, A.V. Borisov, Note on the almost complex manifolds with Norden metric. Comput. Rend. Acad. Bulg. Sci. 39, 31–34 (1986)MathSciNetzbMATHGoogle Scholar
  8. 8.
    K. Gribachev, M. Manev, D. Mekerov, A Lie group as a 4-dimensional quasi-Kahler manifold with Norden metric. JP J. Geom. Topol. 6, 55–68 (2006)MathSciNetzbMATHGoogle Scholar
  9. 9.
    M. Iscan, A. Salimov, On Kähler-Norden manifolds. Proc. Indian Acad. Sci. (Math. Sci.) 119(1), 71–80 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    A.P. Norden, On a class of four-dimensional A-spaces. (Russian) Izv. Vyssh. Uchebn. Zaved. Matematika 17(4), 145–157 (1960)MathSciNetGoogle Scholar
  11. 11.
    M. Obata, Affine connections on manifolds with almost complex, quaternion or Hermitian structure. Jpn. J. Math. 26, 43–77 (1956)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    A. Salimov, On anti-Hermitian metric connections. C. R. Math. Acad. Sci. Paris 352(9), 731–735 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    A. Salimov, S. Turanli, Curvature properties of anti-Kähler-Codazzi manifolds. C. R. Math. Acad. Sci. Paris 351(5–6), 225–227 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    S. Tachibana, Analytic tensor and its generalization. Tohoku Math. J. 12(2), 208–221 (1960)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    V.V. Vishnevskii, Integrable affinor structures and their plural interpretations. J. Math. Sci. (N. Y.) 108(2), 151–187 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    K. Yano, Differential Geometry on Complex and Almost Complex Spaces (Pergamon Press, New York, 1965)zbMATHGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Department of Algebra and GeometryBaku State UniversityBakuAzerbaijan

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