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Conformal semi-slant submersions from Sasakian manifolds

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Abstract

In this paper, we introduce conformal semi-slant submersions from Sasakian manifolds onto Riemannian manifolds. We investigate integrability of distributions and the geometry of leaves of such submersions from Sasakian manifolds onto Riemannian manifolds. Moreover, we examine necessary and sufficient conditions for such submersions to be totally geodesic where characteristic vector field \(\xi\) is vertical.

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References

  1. Akyol, M.A. 2017. Conformal semi-slant submersions. International Journal of Geometric Methods in Modern Physics 14: 1750114.

    Article  MathSciNet  MATH  Google Scholar 

  2. Akyol, M.A., and B. Sahin. 2017. Conformal semi-invariant submersions. Communications in Contemporary Mathematics 19: 1650011.

    Article  MathSciNet  MATH  Google Scholar 

  3. Akyol, M.A., and B. Sahin. 2019. Conformal slant submersions. Hacettepe Journal of Mathematics and Statistics 48(1): 28–44.

    MathSciNet  MATH  Google Scholar 

  4. Altafini, C. 2004. Redundant robotic chains on Riemannian submersions. IEEE Transactions on Robotics and Automation 20: 335–340.

    Article  Google Scholar 

  5. Baird, P., and J.C. Wood. 2003. Harmonic morphisms between Riemannian manifolds. London mathematical society monographs, vol. 29. Oxford/London: Oxford University Press/The Clarendon Press.

    MATH  Google Scholar 

  6. Blair, D.E. 2002. Riemannian geometry of contact and symplectic manifolds. Progress in Mathematics 203. Boston: Birkhäuser.

    Book  Google Scholar 

  7. Bourguignon, J.P., and H.B. Lawson. 1981. Stability and isolation phenomena for Yang–Mills fields. Communications in Mathematical Physics 79: 189–230.

    Article  MathSciNet  MATH  Google Scholar 

  8. Bourguignon, J.P., and H.B. Lawson. 1989. A mathematician’s visit to Kaluza–Klein theory. Rendiconti del Seminario Matematico Universitá e Politecnico di Torino Special Issue 1: 143–163.

    MathSciNet  MATH  Google Scholar 

  9. Chinea, D. 1985. Almost contact metric submersions. Rendiconti del Circolo Matematico di Palermo 34: 89–104.

    Article  MathSciNet  MATH  Google Scholar 

  10. Fuglede, B. 1978. Harmonic morphisms between Riemannian manifolds. Annales de l’Institut Fourier 28: 107–144.

    Article  MathSciNet  MATH  Google Scholar 

  11. Falcitelli, M., S. Ianus, and A.M. Pastore. 2004. Riemannian submersions and related topics. River Edge: World Scientific.

    Book  MATH  Google Scholar 

  12. Gautam, U.K., A. Haseeb, and R. Prasad. 2019. Some results on projective curvature tensor in Sasakian manifolds. Communications of the Korean Mathematical Society 34: 881–896.

    MathSciNet  MATH  Google Scholar 

  13. Gudmundsson, S., and J.C. Wood. 1997. Harmonic morphisms between almost Hermitian manifolds. Bollettino dell’Unione Matematica Italiana (BUMI) 11(2): 185–197.

    MathSciNet  MATH  Google Scholar 

  14. Gray, A. 1967. Pseudo-Riemannian almost product manifolds and submersions. Journal of Mathematics and Mechanics 16: 715–737.

    MathSciNet  MATH  Google Scholar 

  15. Ianus, S., and M. Visinescu. 1987. Kaluza–Klein theory with scalar fields and generalized Hopf manifolds. Classical and Quantum Gravity 4: 1317–1325.

    Article  MathSciNet  MATH  Google Scholar 

  16. Ianus, S., and M. Visinescu. 1991. Space-time compactication and Riemannian submersions. In The mathematical heritage of C. F. Gauss, ed. G. Rassias, 358–371. River Edge: World Scientific.

    Chapter  Google Scholar 

  17. Ianus, S., M. Visinescu, R. Mazzocco, and G.E. Vilcu. 2011. Riemannian submersions from almost contact metric manifolds. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 81: 101–114.

    Article  MathSciNet  MATH  Google Scholar 

  18. Kumar, S., R. Prasad, and P.K. Singh. 2019. Conformal semi-slant submersions from Lorentzian para Sasakian manifolds. Communications of the Korean Mathematical Society 34: 637–655.

    MathSciNet  MATH  Google Scholar 

  19. Mustafa, M.T. 2000. Applications of harmonic morphisms to gravity. Journal of Mathematical Physics 41: 6918–6929.

    Article  MathSciNet  MATH  Google Scholar 

  20. O’Neill, B. 1966. The fundamental equations of a submersion. Michigan Mathematical Journal 13: 458–469.

    MathSciNet  MATH  Google Scholar 

  21. Park, K.S., and R. Prasad. 2013. Semi-slant submersions. Bulletin of the Korean Mathematical Society 50: 951–962.

    Article  MathSciNet  MATH  Google Scholar 

  22. Prasad, R., and S. Kumar. 2019. Conformal semi-invariant submersions from almost contact metric manifolds onto Riemannian manifolds. Khayyam Journal of Mathematics 5: 77–95.

    MathSciNet  MATH  Google Scholar 

  23. Sahin, B. 2010. Anti-invariant Riemannian submersions from almost Hermitian manifolds. Central European Journal of Mathematics 8: 437–447.

    Article  MathSciNet  MATH  Google Scholar 

  24. Sahin, B. 2011. Slant submersions from almost Hermitian manifolds. Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie 54(102): 93–105.

    MathSciNet  MATH  Google Scholar 

  25. Watson, B. 1976. Almost Hermitian submersions. Journal of Differential Geometry 11(1): 147–165.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

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

    Shushil Kumar & Rajendra Prasad

  2. Department of Mathematics, Faculty of Science, Jazan University, 2097, Jazan, Kingdom of Saudi Arabia

    Abdul Haseeb

Authors
  1. Shushil Kumar
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  2. Rajendra Prasad
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  3. Abdul Haseeb
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Correspondence to Abdul Haseeb.

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Communicated by S. Ponnusamy.

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Kumar, S., Prasad, R. & Haseeb, A. Conformal semi-slant submersions from Sasakian manifolds. J Anal 31, 1855–1872 (2023). https://doi.org/10.1007/s41478-022-00540-9

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  • DOI: https://doi.org/10.1007/s41478-022-00540-9

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