Skip to main content

Some remarks concerning hyperholomorphic B-manifolds


The authors consider a differentiable manifold with Π-structure which is an isomorphic representation of an associative, commutative and unitial algebra. For Riemannian metric tensor fields, the Φ-operators associated with r-regular Π-structure are introduced. With the help of Φ-operators, the hyperholomorphity condition of B-manifolds is established.

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


  1. Etayo, F. and Santamaria, R., (J 2 = ±1)-metric manifolds, Publ. Math. Debrecen, 57(3–4), 2000, 435–444.

    MATH  MathSciNet  Google Scholar 

  2. Evtushik, L. E., Lumiste, Ju. G., Ostianu, N. M. et al, Differential-geometric structures on manifolds (in Russian), Problems in Geometry, Vol. 9, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Akad. Nauk SSSR, Moscow, 1979.

    Google Scholar 

  3. Kruchkovich, G. I., Hypercomplex structure on manifold I, Tr. Sem. Vect. Tens. Anal., 16, 1972, 174–201.

    Google Scholar 

  4. Norden, A. P., On a certain class of four-dimensional A-spaces, Izv. Vuzov. Mat., 4, 1960, 145–157.

    MathSciNet  Google Scholar 

  5. Salimov, A. A., Almost ψ-holomorphic tensors and their properties (in Russian), Dokl. Akad. Nauk, 324(3), 1992, 533–536.

    MathSciNet  Google Scholar 

  6. Salimov, A. A., Lifts of poly-affinor structures on pure sections of a tensor bundle, Russian Math. (Iz. VUZ, Mat.), 40(10), 1996, 52–59.

    MATH  MathSciNet  Google Scholar 

  7. Salimov, A. A., Iscan, M. and Etayo, F., Paraholomorphic B-manifold and its properties, Topol. Its Appl., 154, 2007, 925–933.

    Article  MATH  MathSciNet  Google Scholar 

  8. Scheffers, G., Verallgemeinerung der Grundlagen der gewöhnlichen komplexen Funktionen, Berichte Sächs. Acad. Wiss., Bd. 45, 1893, 828–842.

    Google Scholar 

  9. Vishnevskii, V. V., Shirokov, A. P. and Shurygin, V. V., Spaces over Algebras (in Russian), Kazan Gos. University Press, Kazan, 1985.

    Google Scholar 

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

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Kursat Akbulut.

Additional information

(Dedicated to the memory of Vladimir Vishnevskii)

Project supported by the Scientific and Technological Research Council of Turkey (No. 108T590).

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Salimov, A., Iscan, M. & Akbulut, K. Some remarks concerning hyperholomorphic B-manifolds. Chin. Ann. Math. Ser. B 29, 631–640 (2008).

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI:


  • Pure tensor field
  • Interior product
  • Holomorphic tensor
  • B-Manifold

2000 MR Subject Classification

  • 53C15
  • 53C25