Skip to main content
SpringerLink
Log in

On Quasi-bi-slant Submersions

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

As a generalization of hemi-slant submersions and semi-slant submersions, we introduce the notion of quasi-bi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds giving some examples and study such submersions from Kähler manifolds onto Riemannian manifolds. We study the geometry of leaves of distributions which are involved in the definition of the submersion. We also obtain conditions for such submersions to be integrable and totally geodesic. Moreover, we give a characterization theorem for proper quasi-bi-slant submersions with totally umbilical fibers.

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. Akyol, M.A., Sahin, B.: Conformal anti-invariant submersions from almost Hermitian manifolds. Turk J. Math. 40, 43–70 (2016)

    Article  MathSciNet  Google Scholar 

  2. Akyol, M.A., Sari, R., Aksoy, E.: Semi-invariant \(\xi ^{\perp }\) riemannian submersions from almost contact metric manifolds. Int. J. Geom. Methods Mod. Phys. 14(5), 1750075 (2017)

    Article  MathSciNet  Google Scholar 

  3. Ali, S., Fatima, T.: Generic riemannian submersions. Tamkang J. Math. 44(4), 395–409 (2013)

    Article  MathSciNet  Google Scholar 

  4. Baird, P., Wood, J.C.: Harmonic Morphism Between Riemannian Manifolds. Oxford Science Publications, Oxford (2003)

    Book  Google Scholar 

  5. Chinea, D.: Almost contact metric submersions. Rendiconti del Circolo Matematico del Palermo 34(1), 89–104 (1985)

    Article  MathSciNet  Google Scholar 

  6. Falcitelli, M., Pastore, A. M., Ianus, S.: Riemannian Submersions and Related Topics. World Scientific Pub. Co. Inc. (2004)

  7. Gray, A.: Pseudo-Riemannian almost product manifolds and submersions. J. Math. Mech. 16, 715–738 (1967)

    MathSciNet  MATH  Google Scholar 

  8. Gündüzalp, Ylmaz: Slant submersions from almost product riemannian manifolds. Turk. J. Math. 37, 863–873 (2013)

    MathSciNet  MATH  Google Scholar 

  9. Ianus, S., Ionescu, A.M., Mocanu, R., Vilcu, G.E.: Riemannian submersions from almost contact metric manifolds. Abh. Math. Semin. Univ. Humbg. 81(1), 101–114 (2011)

    Article  MathSciNet  Google Scholar 

  10. Ianus, S., Mazzocco, R., Vilcu, G.E.: Riemannian submersion from quaternionic manifolds. Acta Appl. Math. 104(1), 83–89 (2008)

    Article  MathSciNet  Google Scholar 

  11. Pointwise slant submersions: Lee, J. W. Lee., Sahin, B. Bull. Korean Math. Soc. 51, 1115–1126 (2014)

    Article  MathSciNet  Google Scholar 

  12. Park, K.S., Prasad, R.: Semi-slant submersions. Bull. Korean Math. Soc 50(3), 951–962 (2013)

    Article  MathSciNet  Google Scholar 

  13. O’Neill, B.: The fundamental equations of a submersion. Mich. Math. J. 33(13), 458–469 (1966)

    MathSciNet  MATH  Google Scholar 

  14. Shahid, M. H., Al-Solamy, F. R., Jun, Jae-Bok., Ahmad, M.: Submersion of semi-invariant submanifolds of trans-sasakian manifold. Bull. Malays. Math. Sci. Soc. (2) 36(1), 63–71 (2013)

  15. Sahin, B.: Anti-invariant Riemannian submersions from almost Hermitian manifolds. Cent. Eur. J. Math. 8(3), 437–447 (2010)

    Article  MathSciNet  Google Scholar 

  16. Sahin, B.: Semi-invariant submersions from almost Hermitian manifolds. Can. Math. Bull. 56(1), 173–183 (2013)

    Article  MathSciNet  Google Scholar 

  17. Sahin, B.: Slant submersions from Almost Hermitian manifolds. Bulletin math ematique de la Societedes Sciences Math ematiques de Roumanie 54 (102). 1, 93–105 (2011)

  18. Sahin, B.: Riemannian submersion from almost Hermitian manifolds. Taiwan. J. Math. 17(2), 629–659 (2013)

    Article  MathSciNet  Google Scholar 

  19. Sahin, B.: Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications. Elsevier, Academic Press (2017)

    MATH  Google Scholar 

  20. Sahin, B.: Anti-invariant Riemannian submersions from almost Hermitian manifolds. Open Math. 8(3), 437–447 (2010)

    MathSciNet  MATH  Google Scholar 

  21. Sayar, C., Özdemir, F., Tastan, H.M.: Pointwise semi-slant submersions whose total manifolds are locally product Riemannian manifolds. Int. J. Maps Math. 1(1), 91–115 (2018)

    MATH  Google Scholar 

  22. Sayar, C., Tastan, H.M., Ozdemir, F., Tripathi, M.M., Generic submersions from Kaehler manifolds, F. et al. Bull. Malays. Math. Sci. Soc. (2019). https://doi.org/10.1007/s40840-018-00716-2

  23. Tastan, H.M.: On Lagrangian submersions. Hacet. J. Math. Stat. 43(6), 993–1000 (2014)

    MathSciNet  MATH  Google Scholar 

  24. Tastan, H.M., Sahin, B., Yanan, S.: Hemi-slant submersions. Mediterr. J. Math. 13(4), 2171–2184 (2016)

    Article  MathSciNet  Google Scholar 

  25. Watson, B.: Almost Hermitian submersions. J. Differ. Geom. 11(1), 147–165 (1976)

    Article  MathSciNet  Google Scholar 

  26. Yano, K., Kon, M.: Structures on Manifolds. World Scientific, Singapore (1984)

    MATH  Google Scholar 

Download references

Acknowledgements

The authors are thankful to the referees for their valuable suggestions.

Author information

Authors and Affiliations

  1. Department of Mathematics and Astronomy, University of Lucknow, Lucknow, Uttar Pradesh, 226007, India

    Rajendra Prasad

  2. Department of Mathematics, University of Allahabad, Allahabad, 211002, India

    S. S. Shukla

  3. Shri Jai Narain Post Graduate College, Lucknow, India

    Sushil Kumar

Authors
  1. Rajendra Prasad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. S. Shukla
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sushil Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rajendra Prasad.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Prasad, R., Shukla, S.S. & Kumar, S. On Quasi-bi-slant Submersions. Mediterr. J. Math. 16, 155 (2019). https://doi.org/10.1007/s00009-019-1434-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00009-019-1434-7

Keywords

Mathematics Subject Classification

Search

Navigation