Geometrical Aspect of Pointwise Semi-Slant Conformal Submersions

Main Article Content

Mohammad Shuaib, Mohd Bilal


The aim of this paper is to define pointwise semi-slant conformal submersions from locally product Riemannian manifolds onto Riemannian manifolds. We investigated the conditions under which the distributions are integrable and the leaves of the distributions defines totally geodesic foliation. Additionally, we examined the concept of pluriharmonicity of pointwise semi-slant conformal submersions. In support of the results we obtained, we present non-trivial examples.

Article Details


  1. M.A. Akyol, Conformal Semi-Slant Submersions, Int. J. Geom. Methods Mod. Phys. 14 (2017), 1750114.
  2. M.A. Akyol, B. Sahin, Conformal Slant Submersions, Hacettepe J. Math. Stat. 48 (2019), 28–44.
  3. M.A. Akyol, B. Sahin, Conformal Anti-Invariant Submersions From Almost Hermitian Manifolds, Turk. J. Math. 40 (2016), 43–70.
  4. M.A. Akyol, B. ¸Sahin, Conformal Semi-Invariant Submersions, Commun. Contemp. Math. 19 (2017), 1650011.
  5. I. Al-Dayel, T. Fatima, S. Deshmukh, M. Shuaib, A Note on Conformal Bi-Slant Submersion From Kenmotsu Manifold, J. Geom. Phys. 190 (2023), 104864.
  6. I. Al-Dayel, M. Shuaib, S. Deshmukh, T. Fatima, φ-Pluriharmonicity in Quasi Bi-Slant Conformal ξ ⊥-Submersions: A Comprehensive Study, AIMS Math. 8 (2023), 21746–21768.
  7. P. Baird, J.C. Wood, Harmonic Morphisms Between Riemannian Manifolds, Oxford University Press, Oxford, (2003).
  8. J.P. Bourguignon, H.B. Lawson Jr., Stability and Isolation Phenomena for Yang-Mills Fields, Comm. Math. Phys. 79 (1981), 189–230.
  9. J.L. Cabrerizo, A. Carriazo, L.M. Fernández, M. Fernández, Slant Submanifolds in Sasakian Manifolds, Glasgow Math. J. 42 (2000), 125–138.
  10. I.K. Erken, C. Murathan, On Slant Riemannian Submersions for Cosymplectic Manifolds, Bull. Korean Math. Soc. 51 (2014), 1749–1771.
  11. M. Falcitelli, S. Ianus, A.M. Pastore, Riemannian submersions and Related Topics, World Scientific, Singapore, (2004).
  12. A. Gray, Pseudo-Riemannian Almost Product Manifolds and Submersions, J. Math. Mech. 16 (1967), 715–737.
  13. B. Fuglede, Harmonic Morphisms Between Riemannian Manifolds, Ann. l’institut Fourier, 28 (1978), 107–144.
  14. S. Gudmundsson, J.C. Wood, Harmonic Morphisms Between Almost Hermitian Manifolds, Boll. Un. Mat. Ital. B (7) 11 (1997), 185–197.
  15. Y. Gündüzalp, Semi-Slant Submersions from Almost Product Riemannian Manifolds, Demonstr. Math. 49 (2016), 345–356.
  16. S. Ianus, M. Visinescu, Kaluza-Klein Theory With Scalar Fields and Generalised Hopf Manifolds, Class. Quantum Grav. 4 (1987), 1317–1325.
  17. T. Ishihara, A Mapping of Riemannian Manifolds Which Preserves Harmonic Functions, J. Math. Kyoto Univ. 19 (1979), 215–229.
  18. K. Kenmotsu, A Class of Almost Contact Riemannian Manifolds, Tohoku Math. J. 24 (1972), 93–103.
  19. T.W. Lee, B. Sahin, Pointwise Slant Submersions, Bull. Korean Math. Soc. 51 (2014), 1115–1126.
  20. M. T. Mustafa, Applications of Harmonic Morphisms to Gravity, J. Math. Phys. 41 (2000), 6918–6929.
  21. Y. Ohnita, On Pluriharmonicity of Stable Harmonic Maps, J. Lond. Math. Soc. s2-35 (1987), 563–568.
  22. B. O’Neill, The Fundamental Equations of a Submersion, Michigan Math. J. 13 (1966), 459–469.
  23. K.S. Park, R. Prasad, Semi-Slant Submersions, Bull. Korean Math. Soc. 50 (2013), 951–962.
  24. R. Prasad, S. Kumar, Conformal Anti-Invariant Submersions From Nearly Kaehler Manifolds, Palestine J. Math. 8 (2019), 234–247.
  25. B. Sahin, Anti-Invariant Riemannian Submersions From Almost Hermitian Manifolds, Centr. Eur. J. Math. 8 (2010), 437–447.
  26. B. Sahin, Semi-invariant Submersions from Almost Hermitian Manifolds, Can. Math. Bull. 56 (2013), 173–183.
  27. B. Sahin, Slant Submersions From Almost Hermitian Manifolds, Bull. Math. Soc. Sci. Math. Roum. 1 (2011), 93–105.
  28. M.A. Akyol, B. ¸SAhin, Conformal Anti-Invariant Submersions From Almost Hermitian Manifolds, Turk. J. Math. 40 (2016), 43–70.
  29. S.A. Sepet, M. Ergüt, Pointwise Slant Submersions From Cosymplectic Manifolds, Turk. J. Math. 40 (2016), 582–593.
  30. M. Shuaib, T. Fatima, A Note on Conformal Hemi-Slant Submersions, Afr. Mat. 34 (2022), 4.
  31. S. Kumar, S. Kumar, S. Pandey, R. Prasad, Conformal Hemi-Slant Submersions From Almost Hermitian Manifolds, Comm. Korean Math. Soc. 35 (2020), 999–1018.
  32. S. Tanno, The Automorphism Groups of Almost Contact Metric Manifolds, Tohoku Math. J. 21 (1969), 21–38.
  33. H.M. Tastan, B. Sahin, S. Yanan, Hemi-Slant Submersions, Mediterr. J. Math. 13 (2015), 2171–2184.
  34. B. Watson, Almost Hermitian Submersions, J. Differ. Geom. 11 (1976), 147–165.
  35. B. Watson, G, G’-Riemannian Submersions and Nonlinear Gauge Field Equations of General Relativity, In: T. Rassias, (ed.) Global Analysis—analysis on Manifolds, Dedicated M. Morse. Teubner-Texte Math., vol. 57, pp. 324–349. Teubner, Leipzig, (1983).