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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 1

Bi-slant $\xi^{\perp}$-Riemannian submersions

Sezin Aykurt Sepet(KIRSEHIR AHI EVRAN UNIVERSITY)0000-0003-1521-6798
Pages
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Publication Date
2022-02-14
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally we give some decomposition theorems for total manifold.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:We introduce bi-slant $\xi^{\perp}$-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds as a generalization of slant and semi-slant $\xi^{\perp}$-Riemannian submersion and present some examples.
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Key Findings & Data:We give the necessary and sufficient conditions for the integration of the distributions used to define the bi-slant $\xi^{\perp}$-Riemannian submersions and examine the geometry of foliations.
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Conclusion & Impact:Finally we give some decomposition theorems for total manifold.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Riemannian submersion · Sasakian manifold · Bi-slant $\xi^{\perp}$- Riemannian submersion

Abstract

We introduce bi-slant $\xi^{\perp}$-Riemannian submersions from Sasakian manifolds onto Riemannian manifolds as a generalization of slant and semi-slant $\xi^{\perp}$-Riemannian submersion and present some examples. We give the necessary and sufficient conditions for the integration of the distributions used to define the bi-slant $\xi^{\perp}$-Riemannian submersions and examine the geometry of foliations. After we obtain necessary and sufficient conditions related to totally geodesicness of such submersion. Finally we give some decomposition theorems for total manifold.

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Cite This Article

Sepet, S. A. (2022). Bi-slant $\xi^{\perp}$-Riemannian submersions. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 1. https://doi.org/10.15672/hujms.882603

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References (32)

  1. M.A. Akyol and Y. Gündüzalp, On the geometry of conformal anti-invariant $\xi^{\perp}$- submersions, Int. J. Maps Math. 1 (1), 50–67, 2018.
  2. M.A. Akyol and R. Sarı, On semi-slant $\xi^{\perp}$-Riemannian submersions, Mediterr. J. Math. 14, 234 (20 pp), 2017.
  3. M.A. Akyol and B. Şahin, Conformal slant submersions, Hacet. J. Math. Stat. 48 (1), 28–44, 2019.
  4. M.A. Akyol, R. Sarı and E. Aksoy, Semi-invariant $\xi^{\perp}$-Riemannian submersions from almost contact metric manifolds, Int. J. Geom. Methods Mod. Phys. 14 (5), 1750074, 2017.
  5. L.S. Alqahtani, M.S. Stankovic and S. Uddin, Warped product bi-slant submanifolds of cosymplectic manifolds, Filomat, 31 (16), 5065–5071, 2017.
  6. S. Aykurt Sepet and M. Ergüt, Pointwise slant submersions from cosymplectic man- ifolds, Turkish J. Math. 40, 582–593, 2016.
  7. P. Baird and J.C. Wood, Harmonic morphisms between Riemannian manifolds, Lon- don Mathematical Society Monographs, Oxford University Press, Oxford, 2003.
  8. J.L. Cabrerizo, A. Carriazo, L.M. Fernandez and M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasgow Math. J. 42, 125–138, 2000.
  9. A. Carriazo, Bi-slant immersions, In Proceeding of the ICRAMS, Kharagpur, India, 88–97, 2000.
  10. B.Y. Chen, Geometry of Slant Submanifolds, Katholieke Universiteit Leuven, Leuven, 1990.
  11. M. Falcitelly, S. Ianus and A.M. Pastore, Riemannian Submersions and Related Topics, World Scientific, River Edge, NJ, 2004.
  12. A. Gray, Pseudo-Riemannian almost product manifolds and submersions, Journal of Mathematics and Mechanics, 16, 715–737, 1967.
  13. Y. Gündüzalp, Slant submersions from almost product Riemannian manifolds, Turk- ish J. Math. 37, 863–873, 2013.
  14. Y. Gündüzalp, Semi-slant submersions from almost product Riemannian manifolds, Demonstratio Math. 49 (3), 345–356, 2016.
  15. Y. Gündüzalp, Slant submersions in paracontact geometry, Hacet. J. Math. Stat. 49 (3), 822–834, 2020.
  16. İ. Küpeli Erken and C. Murathan, Slant Riemannian submersions from Sasakian manifolds, Arab. J. Math. Sci. 22, 250–264, 2016.
  17. J.W. Lee, Anti-invariant $\xi^{\perp}$-Riemannian submersions from almost contact manifolds. Hacet. J. Math. Stat. 42 (3), 231–241, 2013.
  18. J.W. Lee, Pointwise slant submersions, Bull. Korean Math. Soc. 51 (4), 1115–1126, 2014.
  19. B. O’Neill, The fundamental equations of a submersion, Michigan Math. J. 13, 458– 469, 1966.
  20. F. Özdemir, C. Sayar and H.M. Taştan, Semi-invariant submersions whose total man- ifolds are locally product Riemannian, Quaest. Math. 40 (7), 909–926, 2017.
  21. K.S. Park and R. Prasad, Semi-slant submersions, Bull. Korean Math. Soc. 50 (3), 951–962, 2013.
  22. R. Prasad, S.S. Shukla and S. Kumar, On Quasi-bi-slant submersions, Mediterr. J. Math. 16, 155 (18 pp), 2019.
  23. C. Sayar, M.A. Akyol and R. Prasad, Bi-slant submersions in complex geometry, Int. J. Geom. Methods Mod. Phys., 17 (4), 2050055, 2020.
  24. C. Sayar, H.M. Taştan, F. Özdemir and M.M. Tripathi, Generic submersions from Kaehler Manifolds, Bull. Malays. Math. Sci. Soc. 43, 809–831, 2020.
  25. B. Şahin, Anti-invariant Riemannian submersions from almost Hermitian manifolds, Cent. Eur. J. Math. 8 (3), 437–447, 2010.
  26. B. Şahin, Semi-invariant Riemannian submersions from almost Hermitian manifolds, Canad. Math. Bull. 56 (1), 173–183, 2011.
  27. B. Şahin, Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie, 54 (102), 93–105, 2011.
  28. B. Şahin, Riemannian submersions, Riemannian maps in Hermitian geometry and their applications, Amsterdam, Netherlands: Elsevier Science Publishing Co., Inc., 2017.
  29. H.M. Taştan, On Lagrangian submersions, Hacet. J. Math. Stat. 43 (6), 993–1000, 2014.
  30. H.M. Taştan, B. Şahin and Ş. Yanan, Hemi-slant submersions, Mediterr. J. Math. 13, 2171–2184, 2016.
  31. S. Uddin, B.Y. Chen and F.R. Al-Solamy, Warped Product Bi-slant Immersions in Kaehler Manifolds, Mediterr. J. Math. 14, 95 (11 pages), 2017.
  32. B. Watson, Almost Hermitian submersions, J. Differential Geom. 11 (1), 147–165, 1976.