Skip to main content
SpringerLink
Log in

Natural diagonal Riemannian almost product and para-Hermitian cotangent bundles

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. Studying the compatibility and the anti-compatibility relations between the determined structures and a natural diagonal metric, we find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. Finally, we prove the characterization theorem for the natural diagonal (almost) para-Kählerian structures on the total space of the cotangent bundle.

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. D.V. Alekseevsky, C. Medori, A. Tomassini: Homogeneous para-Kähler Einstein manifolds. Russ. Math. Surv. 64 (2009), 1–43.

    Article  MATH  Google Scholar 

  2. M. Anastasiei: Some Riemannian almost product structures on tangent manifold. Proceedings of the 11th National Conference on Finsler, Lagrange and Hamilton Geometry (Craiova, 2000). Algebras Groups Geom. 17 (2000), 253–262.

    MathSciNet  MATH  Google Scholar 

  3. C. Bejan: A classification of the almost parahermitian manifolds. Differential Geometry and Its Application. Proc. Conf. Dubrovnik/Yougosl. 1988, 1989, pp. 23–27.

  4. C. Bejan: Almost parahermitian structures on the tangent bundle of an almost para-co-Hermitian manifold. Finsler and Lagrange Spaces, Proc. 5th Natl. Semin., Braşov, 1988. Soc. Štiinťe Math. R. S. România, Bucharest, 1989, pp. 105–109.

  5. C. Bejan, L. Ornea: An example of an almost hyperbolic Hermitian manifold. Int. J. Math. Math. Sci. 21 (1998), 613–618.

    Article  MathSciNet  MATH  Google Scholar 

  6. V. Cruceanu: Selected Papers. Editura PIM, Iaši, 2006.

    Google Scholar 

  7. S. L. Druţǎ: Cotangent bundles with general natural Kähler structures. Rev. Roum. Math. Pures Appl. 54 (2009), 13–23.

    Google Scholar 

  8. P.M. Gadea, J. M. Masqué: Classification of almost para-Hermitian manifolds. Rend. Mat. Appl. 11 (1991), 377–396.

    MathSciNet  MATH  Google Scholar 

  9. H.K. Farran, M. S. Zanoun: On hyperbolic Hermite manifolds. Publ. Inst. Math., Nouv. Sér. 46 (1989), 173–182.

    MathSciNet  Google Scholar 

  10. A. Heydari, E. Peyghan: A characterization of the infinitesimal conformal transformations on tangent bundles. Bull. Iran. Math. Soc. 34 (2008), 59–70.

    MathSciNet  MATH  Google Scholar 

  11. S. Ivanov, S. Zamkovoy: Para-Hermitian and paraquaternionic manifolds. Differ. Geom. Appl. 23 (2005), 205–234.

    Article  MathSciNet  MATH  Google Scholar 

  12. I. Kolář: On cotangent bundles of some natural bundles. Geometry and physics. Proc. of the Winter School of Geometry and Physics (Zdíkov, 1993). Rend. Circ. Mat. Palermo Suppl. 37 (1994), 115–120.

    Google Scholar 

  13. I. Kolář, P.W. Michor, J. Slovák: Natural Operations in Differential Geometry. Springer, Berlin, 1993.

    MATH  Google Scholar 

  14. O. Kowalski, M. Sekizawa: Natural transformations of Riemannian metrics on manifolds to metrics on tangent bundles-a classification. Bull. Tokyo Gakugei Univ., Sect. IV 40 (1988), 1–29.

    MathSciNet  Google Scholar 

  15. D. Luczyszyn, Z. Olszak: On paraholomorphically pseudosymmetric para-Kählerian manifolds. J. Korean Math. Soc. 45 (2008), 953–963.

    Article  MathSciNet  MATH  Google Scholar 

  16. D. Mekerov: On Riemannian almost product manifolds with nonintegrable structure. J. Geom. 89 (2008), 119–129.

    Article  MathSciNet  MATH  Google Scholar 

  17. I. Mihai, C. Nicolau: Almost product structures on the tangent bundle of an almost paracontact manifold. Demonstr. Math. 15 (1982), 1045–1058.

    MathSciNet  MATH  Google Scholar 

  18. K.-P. Mok, E.M. Patterson, Y.-C. Wong: Structure of symmetric tensors of type (0,2) and tensors of type (1,1) on the tangent bundle. Trans. Am. Math. Soc. 234 (1977), 253–278.

    MathSciNet  MATH  Google Scholar 

  19. M.-I. Munteanu: CR-structures on the unit cotangent bundle and Bochner type tensor. An. Štiinť. Univ. Al. I. Cuza Iaši A, Ser. Nouǎ, Mat. 44 (1998), 125–136.

    MathSciNet  MATH  Google Scholar 

  20. A.M. Naveira: A classification of Riemannian almost product manifolds. Rend. Math. Appl. VII. Ser. 3 (1983), 577–592.

    MathSciNet  MATH  Google Scholar 

  21. V. Oproiu, N. Papaghiuc: A pseudo-Riemannian structure on the cotangent bundle. An. Štiinť. Univ. Al. I. Cuza Iaši, Ser. Nouǎ Mat. 36 (1990), 265–276.

    MathSciNet  MATH  Google Scholar 

  22. V. Oproiu, N. Papaghiuc, G. Mitric: Some classes of parahermitian structures on cotangent bundles. An. Štiinť. Univ. Al. I. Cuza Iaši, Ser. Nouǎ Mat. 43 (1996), 7–22.

    MathSciNet  MATH  Google Scholar 

  23. V. Oproiu, D.D. Porošniuc: A class of Kähler Einstein structures on the cotangent bundle. Publ. Math. 66 (2005), 457–478.

    MATH  Google Scholar 

  24. E. Peyghan, A. Heydari: A class of locally symmetric para-Kähler Einstein structures on the cotangent bundle. Int. Math. Forum 5 (2010), 145–153.

    MathSciNet  MATH  Google Scholar 

  25. M.T. Staikova, K. I. Gribachev: Canonical connections and conformal invariants on Riemannian almost-product manifolds. Serdica 18 (1992), 150–161.

    MathSciNet  MATH  Google Scholar 

  26. K. Yano: Differential Geometry on a Complex and Almost Complex Spaces. Pergamon Press, Oxford-London-New York-Paris-Frankfurt, 1965.

    Google Scholar 

  27. K. Yano, S. Ishihara: Tangent and Cotangent Bundles. Marcel Dekker Inc., New York, 1973.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Sciences, Universitatea “Alexandru Ioan Cuza” din, 54 Lascar Catargi Street, RO-700107, Iaşi, Romania

    Simona-Luiza Druţǎ-Romaniuc

Authors
  1. Simona-Luiza Druţǎ-Romaniuc
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Simona-Luiza Druţǎ-Romaniuc.

Additional information

The author was supported by the Program POSDRU/89/1.5/S/49944, Universitatea “Alexandru Ioan Cuza” din Iaşi, Romania.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Druţǎ-Romaniuc, SL. Natural diagonal Riemannian almost product and para-Hermitian cotangent bundles. Czech Math J 62, 937–949 (2012). https://doi.org/10.1007/s10587-012-0075-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10587-012-0075-9

Keywords

MSC 2010

Search

Navigation