Taiwanese Journal of Mathematics

$H$-SEMI-SLANT SUBMERSIONS FROM ALMOST QUATERNIONIC HERMITIAN MANIFOLDS

Kwang-Soon Park

Full-text: Open access

Abstract

As a generalization of semi-slant submersions, h-slant submersions, and h-semi-invariant submersions, we introduce the notions of h-semi-slant submersions and almost h-semi-slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds. We obtain characterizations and investigate the integrability of distributions, the geometry of fibers, and the harmonicity of such maps. We also find a condition for such maps to be totally geodesic. Moreover, we give some examples of such maps.

Article information

Source
Taiwanese J. Math., Volume 18, Number 6 (2014), 1909-1926.

Dates
First available in Project Euclid: 21 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500667503

Digital Object Identifier
doi:10.11650/tjm.18.2014.4079

Mathematical Reviews number (MathSciNet)
MR3284038

Zentralblatt MATH identifier
1357.53052

Subjects
Primary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C26: Hyper-Kähler and quaternionic Kähler geometry, "special" geometry

Keywords
Riemannian submersion slant angle integrable totally geodesic

Citation

Park, Kwang-Soon. $H$-SEMI-SLANT SUBMERSIONS FROM ALMOST QUATERNIONIC HERMITIAN MANIFOLDS. Taiwanese J. Math. 18 (2014), no. 6, 1909--1926. doi:10.11650/tjm.18.2014.4079. https://projecteuclid.org/euclid.twjm/1500667503


Export citation

References

  • D. V. Alekseevsky and S. Marchiafava, Almost complex submanifolds of quaternionic manifolds, in: Proceedings of the Colloquium on Differential Geometry, Debrecen (Hungary), 25-30 July 2000; Inst. Math. Inform. Debrecen, 2001, pp. 23-38.
  • A. L. Besse, Einstein Manifolds, Springer Verlag, Berlin, 1987.
  • M. Barros, B. Y. Chen and F. Urbano, Quaternion CR-submanifolds of quaternion manifolds, Kodai Mathematical Journal, 4 (1980), 399-417.
  • J. P. Bourguignon and H. B. Lawson, A mathematician's visit to Kaluza-Klein theory, Rend. Semin. Mat. Torino Fasc. Spec., (1989), 143-163.
  • J. P. Bourguignon and H. B. Lawson, Stability and isolation phenomena for Yang-mills fields, Commum. Math. Phys. 79 (1981), 189-230.
  • P. Baird and J. C. Wood, Harmonic Morphisms between Riemannian Manifolds, Oxford Science Publications, 2003.
  • B. Y. Chen, Geometry of Slant Submaniflods, Katholieke Universiteit Leuven, Leuven, 1990.
  • V. Cortés, C. Mayer, T. Mohaupt and F. Saueressig, Special geometry of Euclidean supersymmetry 1. Vector multiplets, J. High Energy Phys., 3 (2004), 028.
  • M. Falcitelli, S. Ianus and A. M. Pastore, Riemannian Submersions and Related Topics, World Scientific Publishing Co., 2004.
  • A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 16 (1967), 715-737.
  • S. Ianus, R. Mazzocco and G. E. Vilcu, Riemannian submersions from quaternionic manifolds, Acta. Appl. Math., 104 (2008), 83-89.
  • S. Ianus and M. Visinescu, Kaluza-Klein theory with scalar fields and generalized Hopf manifolds, Class. Quantum Gravity, 4 (1987), 1317-1325.
  • S. Ianus and M. Visinescu, Space-time compactification and Riemannian submersions, in: The Mathematical Heritage of C. F. Gauss, Rassias, G. (ed.), World Scientific, River Edge., 1991, pp. 358-371.
  • M. T. Mustafa, Applications of harmonic morphisms to gravity, J. Math. Phys., 41(10) (2000), 6918-6929.
  • B. O'Neill, The fundamental equations of a submersion, Mich. Math. J., 13 (1966), 458-469.
  • K. S. Park, H-slant submersions, Bull. Korean Math. Soc., 49(2) (2012), 329-338.
  • K. S. Park, H-semi-invariant submersions, Taiwan. J. Math., 16(5) (2012), 1865-1878.
  • K. S. Park and R. Prasad, Semi-slant submersions, Bull. Korean Math. Soc., 50(3) (2013), 951-962.
  • B. Sahin, Anti-invariant Riemannian submersions from almost Hermitian manifolds, Cent. Eur. J. Math., 8(3) (2010), 437-447.
  • B. Sahin, Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie Tome, 54(1) (102) (2011), 93-105.
  • B. Sahin, Semi-invariant submersions from almost Hermitian manifolds, Canad. Math. Bull., 56(1) (2013), 173-183.
  • B. Sahin, Riemannian submersions from almost Hermitian manifolds, Taiwanese J. Math., 17(2) (2013), 629-659.
  • B. Watson, Almost Hermitian submersions, J. Differential Geom., 11(1) (1976), 147-165.
  • B. Watson, $G,G'$-Riemannian submersions and nonlinear gauge field equations of general relativity, in: Global Analysis - Analysis on Manifolds, Rassias, T. (ed.), dedicated M. Morse. Teubner-Texte Math., 57 (1983), 324-349, Teubner, Leipzig.