Skip to main content
SpringerLink
Log in

Hermitian f-structures on 6-dimensional filiform Lie groups

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We consider left-invariant f-structures on 6-dimensional filiform Lie groups and present sufficient conditions under which special left-invariant f-structures on these Lie groups belong to the class of Hermitian f-structures. We also give particular examples of the corresponding f-structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Balashchenko, V. V., Nikonorov, Yu. G. Rodionov, E. D., and Slavskii, V. V. Homogeneous Spaces: Theory and Applications (Poligrafist, Khanty-Mansiysk, 2008) [in Russian].

    Google Scholar 

  2. Yano, K. “On a Structure Defined by a Tensor Field f of Type (1, 1) Satisfying f 3 + f = 0”, Tensor 14, 99–109 (1963).

    MathSciNet  MATH  Google Scholar 

  3. Kirichenko, V. F. “Methods of Generalized HermitianGeometry in the Theory of ContactManifolds”, in Itogi Nauki i Tekhn. Problemy Geometrii (VINITI,Moscow, 1986) Vol. 18, pp. 252–71 [in Russian].

    Google Scholar 

  4. Stepanov, N. A. “Basic Facts of the Theory of ϕ-Spaces”, Iz. VUZ. Matematika, No. 3, 88–95 (1967). [in Russian]

    MathSciNet  Google Scholar 

  5. Fedenko, A. S. Spaces with Symmetries (Belarusian University, Minsk, 1977) [in Russian].

    MATH  Google Scholar 

  6. Kowalski, O. Generalized Symmetric Spaces (Springer, Berlin, 1980; Mir,Moscow, 1984).

    MATH  Google Scholar 

  7. Balashchenko, V. V. and Stepanov, N. A. “Canonical Affinor Structures of Classical Type on Regular Φ-spaces”, Sb.Math. 186, No. 11, 1551–1580 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  8. Balashchenko, V. V. “Canonical f-Structure of Hyperbolic Type on Regular Φ-spaces”, Russ. Math. Surv. 53, No. 4, 861–863 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  9. Kaplan, A. “Riemannian Nilmanifolds Attached to Clifford Modules”, Geom.Dedicata 11, No. 2, 127–136 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  10. Kaplan, A. “On the Geometry of Groups of Heisenberg Type”, Bull. London Math. Soc. 15, No. 1, 35–42 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  11. Balashchenko, V. V. “Invariant Structures on the 6-Dimensional Generalized Heisenberg Group”, Kragujevac J.Math. 35, No. 2, 209–222 (2011).

    MathSciNet  MATH  Google Scholar 

  12. Balashchenko V. V. and Dubovik, P. A. “Left-Invariant f-Structures on the 5-Dimensional Heisenberg Group H(2, 1)”, Vestnik Belarusian Univ. Ser. 1. Matem., Fiz., Inform., No. 3, 112–117 (2013).

    MATH  Google Scholar 

  13. Balashchenko, V. V. “HomogeneousHermitian f-Manifolds”, Russ. Math. Surv. 56, No. 3, 575–577 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  14. Yano, K. and Kon, M. CR Submanifolds of Kählerian and SasakianManifolds (Boston, Birkhäser, 1983; Nauka, Moscow, 1990).

    Google Scholar 

  15. Kirichenko, V. F. “Quasihomogeneous Manifolds and Generalized Almost Hermitian Structures”, Izv. Akad. Nauk SSSR, Ser.Mat. 47, No. 6, 1208–1223 (1983) [in Russian].

    MathSciNet  MATH  Google Scholar 

  16. Helgason, S. Differential Geometry and Symmetric Spaces (Academic Press, NY, 1962; Mir, Moscow, 1964).

    MATH  Google Scholar 

  17. Kobayashi, S. and Nomizu, K. Foundations of Differential Geometry (Interscience Publishers, NY, 1969; Nauka, Moscow, 1981), Vol. 2.

    MATH  Google Scholar 

  18. Khakimdjanov, Yu., Goze, M., and Medina, A. “Sympletic or Contact Structures on Lie Groups”, Differential Geometry Appl. 21, No. 1, 41–54 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  19. Vergne, M. “Cohomologie des Algèbres de Lie Nilpotentes. Application àl’étude de la Variétédes Algèbres de Lie Nilpotentes”, Bull. Soc. Math. France 98, No. 1, 81–116 (1970).

    MathSciNet  MATH  Google Scholar 

  20. Morozov, V. V. “Classification of Nilpotent Lie Algebras of Sixth Order”, Iz. VUZ.Matematika, No. 4, 161–171 (1958) [in Russian].

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Belarusian State University, pr. Nezavisimosti 4, Minsk, 220030, Republic of Belarus

    P. A. Dubovik

Authors
  1. P. A. Dubovik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. A. Dubovik.

Additional information

Original Russian Text © P.A. Dubovik, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 7, pp. 34–43.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dubovik, P.A. Hermitian f-structures on 6-dimensional filiform Lie groups. Russ Math. 60, 29–36 (2016). https://doi.org/10.3103/S1066369X16070057

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X16070057

Keywords

Search

Navigation