• Received : 2012.04.19
  • Published : 2013.05.31


We introduce semi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of slant submersions, semi-invariant submersions, anti-invariant submersions, etc. We obtain characterizations, investigate the integrability of distributions and the geometry of foliations, etc. We also find a condition for such submersions to be harmonic. Moreover, we give lots of examples.


Riemannian submersion;slant angle;harmonic map;totally geodesic


  1. M. T. Mustafa, Applications of harmonic morphisms to gravity, J. Math. Phys. 41 (2000), no. 10, 6918-6929.
  2. B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 458-469.
  3. K. S. Park, H-slant submersions, Bull. Korean Math. Soc. 49 (2012), no. 2, 329-338.
  4. K. S. Park, H-semi-invariant submersions, Taiwan. J. Math. 16 (2012), no. 5, 1865-1878.
  5. B. Sahin, Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie Tome 54(102) (2011), no. 1, 93-105.
  6. B. Sahin, Semi-invariant submersions from almost Hermitian manifolds, Canad. Math. Bull. 56 (2013), no. 1, 173-183.
  7. B. Sahin, Anti-invariant Riemannian submersions from almost Hermitian manifolds, Cent. Eur. J. Math. 8 (2010), no. 3, 437-447.
  8. B. Watson, Almost Hermitian submersions, J. Differential Geom. 11 (1976), no. 1, 147-165.
  9. B. Watson, G,G'-Riemannian submersions and nonlinear gauge field equations of general relativity, In: Rassias, T. (ed.) Global Analysis - Analysis on manifolds, dedicated M. Morse, Teubner-Texte Math. 57 (1983), 324-349, Teubner, Leipzig.
  10. J. P. Bourguignon and H. B. Lawson, A mathematician's visit to Kaluza-Klein theory, Rend. Sem. Mat. Univ. Politec. Torino 1989, Special Issue, 143-163 (1990).
  11. J. P. Bourguignon and H. B. Lawson, Stability and isolation phenomena for Yang-mills fields, Comm. Math. Phys. 79 (1981), no. 2, 189-230.
  12. P. Baird and J. C. Wood, Harmonic Morphisms between Riemannian Manifolds, Oxford science publications, 2003.
  13. B. Y. Chen, Geometry of Slant Submaniflods, Katholieke Universiteit Leuven, Leuven, 1990.
  14. V. Cortes, C. Mayer, T. Mohaupt, and F. Saueressig, Special geometry of Euclidean supersymmetry. I. Vector multiplets, J. High Energy Phys. (2004), no. 3, 028, 73 pp.
  15. M. Falcitelli, S. Ianus, and A. M. Pastore, Riemannian Submersions and Related Topics, World Scientific Publishing Co., 2004.
  16. A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech 16 (1967), 715-737.
  17. S. Ianus, A. M. Ionescu, R.Mazzocco, G. E. Vilcu, Riemannian submersions from almost contact metric manifolds, Abh. Math. Semin. Univ. Hamb. 81 (2011), no. 1, 101-114.
  18. S. Ianus, R. Mazzocco, and G. E. Vilcu, Riemannian submersions from quaternionic manifolds, Acta Appl. Math. 104 (2008), no. 1, 83-89.
  19. S. Ianus and M. Visinescu, Kaluza-Klein theory with scalar fields and generalised Hopf manifolds, Classical Quantum Gravity 4 (1987), no. 5, 1317-1325.
  20. S. Ianus and M. Visinescu, Space-time compactification and Riemannian submersions, In: Rassias, G.(ed.) The Mathematical Heritage of C. F. Gauss, 358-371, World Scientific, River Edge, 1991.
  21. A. Bejancu, Geometry of CR-submanifolds, Kluwer Academic, 1986.

Cited by

  2. Conformal semi-slant submersions vol.14, pp.07, 2017,
  3. Semi-slant Riemannian map 2017,
  4. Hemi-Slant Submersions vol.13, pp.4, 2016,
  5. Conformal semi-invariant submersions vol.19, pp.02, 2017,
  6. On anti-invariant Riemannian submersions whose total manifolds are locally product Riemannian vol.108, pp.2, 2017,
  7. Semi-invariant submersions whose total manifolds are locally product Riemannian 2017,
  8. Almost h-semi-slant Riemannian maps to almost quaternionic Hermitian manifolds vol.17, pp.06, 2015,