Some remarks concerning Riemannian extensions

We study some properties of Riemannian extensions in cotangent bundles with the help of adapted frames.

This is a preview of subscription content, access via your institution.


  1. 1.

    E. M. Patterson and A. G. Walker, “Riemannian extensions,” Quant. J. Math., 3, 19–28 (1952).

    Article  MathSciNet  MATH  Google Scholar 

  2. 2.

    K. Yano and Sh. Ishihara, “Tangent and cotangent bundles: Differential geometry,” Pure Appl. Math., No. 16 (1973).

  3. 3.

    V. Dryuma, “On Riemannian extension of the Schwarzschild metric,” Bull. Acad. Şti. Rep. Mold. Mat., No. 3, 92–103 (2003).

  4. 4.

    V. Dryuma, “The Riemannian extension in theory of differential equations and their application,” Mat. Fiz. Anal. Geom., 10, No. 3, 307–325 (2003).

    MathSciNet  MATH  Google Scholar 

  5. 5.

    G. T. Ganchev and A. V. Borisov, “Note on the almost complex manifolds with a Norden metric,” C. R. Acad. Bulg. Sci., 39, No. 5, 31–34 (1986).

    MathSciNet  MATH  Google Scholar 

  6. 6.

    M. Iscan and A. A. Salimov, On Kähler – Norden manifolds,” Proc. Indian Acad. Sci. (Math. Sci.), 119, No. 1, 71–80 (2009).

    MathSciNet  MATH  Google Scholar 

  7. 7.

    M. Manev and D. Mekerov, “On Lie groups as quasi-Kähler manifolds with Killing Norden metric,” Adv. Geom., 8, No. 3, 343–352 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  8. 8.

    A. A. Salimov, M. Iscan, and F. Etayo, “Paraholomorphic B-manifold and its properties,” Topol. Appl., 154, 925–933 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  9. 9.

    A. A. Salimov, M. Iscan, and K. Akbulut, “Some remarks concerning hyperholomorphic B-manifolds,” Chin. Ann. Math., 29, No. 6, 631–640 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  10. 10.

    V. V. Vishnevskii, “Integrable affinor structures and their plural interpretations,” J. Math. Sci., 108, No. 2, 151–187 (2002).

    Article  MathSciNet  Google Scholar 

  11. 11.

    G. I. Kruchkovich, “Hypercomplex structures on a manifold, I,” Trudy Sem. Vect. Tens. Anal. Moscow Univ., 16, 174–201 (1972).

    Google Scholar 

  12. 12.

    A. A. Salimov, Generalized Yano –Ako operator and the complete lift of tensor fields,” Tensor (N.S.), 55, No. 2, 142–146 (1994).

    MathSciNet  MATH  Google Scholar 

  13. 13.

    A. A. Salimov, “Lifts of poly-affinor structures on pure sections of a tensor bundle,” Rus. Math. (Izv. Vuzov), 40, No. 10, 52–59 (1996).

    MathSciNet  MATH  Google Scholar 

  14. 14.

    V. V. Vishnevskii, A. P. Shirokov, and V. V. Shurygin, Spaces over Algebras, Kazan Gos. Univ., Kazan (1985).

    Google Scholar 

  15. 15.

    K. Yano and M. Ako, “On certain operators associated with tensor fields,” Kodai Math. Semin. Repts, 20, 414–436 (1968).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to S. Aslanci.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 5, pp. 579–590, May, 2010.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Aslanci, S., Kazimova, S. & Salimov, A.A. Some remarks concerning Riemannian extensions. Ukr Math J 62, 661–675 (2010).

Download citation


  • Vector Field
  • Complex Manifold
  • Tensor Field
  • Cotangent Bundle
  • Horizontal Lift