Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

CONFORMAL SEMI-SLANT SUBMERSIONS FROM LORENTZIAN PARA SASAKIAN MANIFOLDS

  • Kumar, Sushil (Department of Mathematics and Astronomy University of Lucknow) ;
  • Prasad, Rajendra (Department of Mathematics and Astronomy University of Lucknow) ;
  • Singh, Punit Kumar (Department of Mathematics and Astronomy University of Lucknow)
  • Received : 2018.04.07
  • Accepted : 2018.11.05
  • Published : 2019.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we introduce conformal semi-slant submersions from Lorentzian para Sasakian manifolds onto Riemannian manifolds. We investigate integrability of distributions and the geometry of leaves of such submersions from Lorentzian para Sasakian manifolds onto Riemannian manifolds. Moreover, we examine necessary and sufficient conditions for such submersions to be totally geodesic where characteristic vector field ${\xi}$ is vertical.

Keywords

References

  1. M. A. Akyol, Conformal semi-slant submersions, Int. J. Geom. Methods Mod. Phys. 14 (2017), no. 7, 1750114, 25 pp. https://doi.org/10.1142/S0219887817501146
  2. M. A. Akyol, Conformal anti-invariant submersions from cosymplectic manifolds, Hacet. J. Math. Stat. 46 (2017), no. 2, 177-192.
  3. M. A. Akyol and B. Sahin, Conformal anti-invariant submersions from almost Hermitian manifolds, Turkish J. Math. 40 (2016), no. 1, 43-70. https://doi.org/10.3906/mat-1408-20
  4. M. A. Akyol and R. Sar, On semi-slant $\xi^{\bot}$-Riemannian submersions, Mediterr. J. Math. 14 (2017), no. 6, Art. 234, 20 pp. https://doi.org/10.1007/s00009-017-1035-2
  5. P. Baird and J. C. Wood, Harmonic morphisms between Riemannian manifolds, London Mathematical Society Monographs. New Series, 29, The Clarendon Press, Oxford University Press, Oxford, 2003.
  6. J.-P. Bourguignon, A mathematician's visit to Kaluza-Klein theory, Rend. Sem. Mat. Univ. Politec. Torino 1989, Special Issue, 143-163 (1990).
  7. J.-P. Bourguignon and H. B. Lawson, Jr., Stability and isolation phenomena for Yang-Mills fields, Comm. Math. Phys. 79 (1981), no. 2, 189-230. https://doi.org/10.1007/BF01942061
  8. J. L. Cab rerizo, A. Carriazo, L. M. Fernandez, and M. Fernandez, Semi-slant submanifolds of a Sasakian manifold, Geom. Dedicata 78 (1999), no. 2, 183-199. https://doi.org/10.1023/A:1005241320631
  9. M. Falcitelli, S. Ianus, and A. M. Pastore, Riemannian submersions and related topics, World Scientific Publishing Co., Inc., River Edge, NJ, 2004.
  10. B. Fuglede, Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble) 28 (1978), no. 2, vi, 107-144. https://doi.org/10.5802/aif.691
  11. S. Gudmundsson and J. C. Wood, Harmonic morphisms between almost Hermitian manifolds, Boll. Un. Mat. Ital. B (7) 11 (1997), no. 2, suppl., 185-197.
  12. Y. Gunduzalp, Slant submersions from Lorentzian almost paracontact manifolds, Gulf J. Math. 3 (2015), no. 1, 18-28.
  13. Y. Gunduzalp, Semi-slant submersions from almost product Riemannian manifolds, Demonstr. Math. 49 (2016), no. 3, 345-356. https://doi.org/10.1515/dema-2016-0029
  14. Y. Gunduzalp and M. A. Akyol, Conformal slant submersions from cosymplectic manifolds, Turk J Math 42 (2018), 2672-2689. https://doi.org/10.3906/mat-1803-106
  15. A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715-737.
  16. S. Ianus and M. Visinescu, Kaluza-Klein theory with scalar fields and generalised Hopf manifolds, Classical Quantum Gravity 4 (1987), no. 5, 1317-1325. https://doi.org/10.1088/0264-9381/4/5/026
  17. S. Ianus and M. Visinescu, Space-time compactification and Riemannian submersions, in The mathematical heritage of C. F. Gauss, 358-371, World Sci. Publ., River Edge, NJ, 1991.
  18. S. Ianus, M. Visinescu, R. Mazzocco, and G. E. Vilcu, Riemannian submersions from almost contact metric manifolds, Abh. Math. Semin. Univ. Hambg. 81 (2011), no. 1, 101-114. https://doi.org/10.1007/s12188-011-0049-0
  19. K. Matsumoto, On Lorentzian paracontact manifolds, Bull. Yamagata Univ. Natur. Sci. 12 (1989), no. 2, 151-156.
  20. I. Mihai and R. Rosca, On Lorentzian P-Sasakian manifolds, in Classical analysis (Kazimierz Dolny, 1991), 155-169, World Sci. Publ., River Edge, NJ, 1992.
  21. I. Mihai, A. A. Shaikh, and U. C. De, On Lorentzian para-Sasakian manifolds, Rendicontidel Seminario Matematicodi Messina 3 (1999), 149-158.
  22. B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459-469. https://doi.org/10.1307/mmj/1028999604
  23. N. Papaghiuc, Semi-slant submanifolds of a Kaehlerian manifold, An. Stiint. Univ. Al. I. Cuza Iasi Sect. I a Mat. 40 (1994), no. 1, 55-61.
  24. K.-S. Park and R. Prasad, Semi-slant submersions, Bull. Korean Math. Soc. 50 (2013), no. 3, 951-962. https://doi.org/10.4134/BKMS.2013.50.3.951
  25. B. Watson, Almost Hermitian submersions, J. Differential Geometry 11 (1976), no. 1, 147-165. https://doi.org/10.4310/jdg/1214433303
  26. M. T. Mustafa, Applications of harmonic morphisms to gravity, J. Math. Phys. 41 (2000), no. 10, 6918-6929. https://doi.org/10.1063/1.1290381