Park, Kwang-Soon

  • Received : 2014.12.19
  • Published : 2016.03.31


We introduce the notions of h-v-semi-slant submersions and almost h-v-semi-slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We obtain characterizations, investigate the integrability of distributions, the geometry of foliations, and a decomposition theorem. We find a condition for such submersions to be totally geodesic. We also obtain an inequality of a h-v-semi-slant submersion in terms of squared mean curvature, scalar curvature, and h-v-semi-slant angle. Finally, we give examples of such maps.


Riemannian submersion;slant angle;integrable;totally geodesic


  1. D. V. Alekseevsky and S. Marchiafava, Almost complex submanifolds of quaternionic manifolds, Steps in differential geometry (Debrecen, 2000), 23-38, Inst. Math. Inform., Debrecen, 2001.
  2. P. Baird and J. C. Wood, Harmonic Morphisms between Riemannian Manifolds, The Clarendon Press, Oxford University Press, Oxford, 2003.
  3. A. L. Besse, Einstein Manifolds, Springer Verlag, Berlin, 1987.
  4. J. P. Bourguignon and H. B. Lawson, Stability and isolation phenomena for Yang-mills fields, Comm. Math. Phys. 79 (1981), no. 2, 189-230.
  5. J. P. Bourguignon and H. B. Lawson, A mathematician's visit to Kaluza-Klein theory, Rend. Sem. Mat. Univ. Politec. Torino (1989), 143-163.
  6. B. Y. Chen, Geometry of Slant Submaniflods, Katholieke Universiteit Leuven, Leuven, 1990.
  7. V. Cortes, C. Mayer, T. Mohaupt, and F. Saueressig, Special geometry of Euclidean supersymmetry 1. Vector multiplets, J. High Energy Phys. (2004), 03, 028.
  8. M. Falcitelli, S. Ianus, and A. M. Pastore, Riemannian Submersions and Related Topics, World Scientific Publishing Co., 2004.
  9. A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715-737.
  10. S. Ianus, A. M. Ionescu, R. Mazzocco, and G. E. Vilcu, Riemannian submersions from almost contact metric manifolds, Abh. Math. Semin. Univ. Hambg. 81 (2011), no. 1, 101-114.
  11. S. Ianus, R. Mazzocco, and G. E. Vilcu, Riemannian submersions from quaternionic manifolds, Acta Appl. Math. 104 (2008), no. 1, 83-89.
  12. S. Ianus and M. Visinescu, Kaluza-Klein theory with scalar fields and generalised Hopf manifolds, Classical Quantum Gravity 4 (1987), no. 5, 1317-1325.
  13. S. Ianus and M. Visinescu, Space-time compactification and Riemannian submersions, In: Rassias, G.(ed.) The Mathematical Heritage of C. F. Gauss, (1991), 358-371, World Scientific, River Edge.
  14. S. Ishihara, Quaternion Kahlerian manifolds, J. Differential Geom. 9 (1974), 483-500.
  15. M. T. Mustafa, Applications of harmonic morphisms to gravity, J. Math. Phys. 41 (2000), no. 10, 6918-6929.
  16. B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 458-469.
  17. K. S. Park, H-slant submersions, Bull. Korean Math. Soc. 49 (2012), no. 2, 329-338.
  18. K. S. Park, H-semi-invariant submersions, Taiwanese J. Math. 16 (2012), no. 5, 1865-1878.
  19. K. S. Park, H-semi-slant submersions from almost quaternionic Hermitian manifolds, Tai-wanese J. Math. 18 (2014), no. 6, 1909-1926.
  20. K. S. Park, V-semi-slant submersions from almost Hermitian manifolds, arXiv: 1206.1404v1 [math.DG].
  21. K. S. Park and R. Prasad, Semi-slant submersions, Bull. Korean Math. Soc. 50 (2013), no. 3, 951-962.
  22. B. Sahin, Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie Tome 54(102) (2011), no. 1, 93-105.
  23. B. Sahin, Semi-invariant submersions from almost Hermitian manifolds, Canad. Math. Bull. 56 (2013), no. 1, 173-183.
  24. B. Watson, Almost Hermitian submersions, J. Differential Geom. 11 (1976), no. 1, 147-165.
  25. 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.

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Supported by : Sogang Research Team for Discrete and Geometric Structures