DOI QR코드

DOI QR Code

CONFORMAL HEMI-SLANT SUBMERSION FROM KENMOTSU MANIFOLD

  • Mohammad Shuaib (Department of Mathematics, Aligarh Muslim University) ;
  • Tanveer Fatima (Department of Mathematics and Statistics, College of Sciences, Taibah University)
  • 투고 : 2022.09.03
  • 심사 : 2022.12.25
  • 발행 : 2023.06.01

초록

As a generalization of conformal semi-invariant submersion, conformal slant submersion and conformal semi-slant submersion, in this paper we study conformal hemi-slant submersion from Kenmotsu manifold onto a Riemannian manifold. The necessary and sufficient conditions for the integrability and totally geodesicness of distributions are discussed. Moreover, we have obtained sufficient condition for a conformal hemi-slant submersion to be a homothetic map. The condition for a total manifold of the submersion to be twisted product is studied, followed by other decomposition theorems.

키워드

과제정보

The authors are thankful to the referee for his/her valuable suggestions and careful reading of the manuscript.

참고문헌

  1. M. A. Akyol, Conformal semi-slant submersions, Int. J. Geom. Methods Mod. Phys. 14 (2017), no. 7, 1750114. 
  2. M. A. Akyol, R. Sari, and E. Aksoy, Semi-invariant ξ-Riemannian submersions from almost contact metric manifolds, Int. J. Geom. Methods Mod. Phys. 14 (2017), no. 5, 1750074. 
  3. M. A. Akyol and B. Sahin, Conformal slant submersions, Hacettepe Journal of Mathematics and Statistics 48 (2019), no. 1, 28-44.  https://doi.org/10.15672/HJMS.2017.506
  4. M. A. Akyol and B. Sahin, Conformal anti-invariant submersions from almost Hermitian manifolds. Turkish Journal of Mathematics (40) (2016), 43-70. 
  5. M. A. Akyol and B. Sahin; Conformal semi-invariant submersions, Communications in Contemporary Mathematics 19 (2017), 1650011. 
  6. 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
  7. J. P. Bourguignon, A mathematician's visit to Kaluza-Klein theory, Rend. Sem. Mat. Univ. Politec. Torino 1989 (1990), Special Issue, 143-163. 
  8. I. K. Erken and C. Murathan, On slant Riemannian submersions for cosymplectic manifolds, Bull. Korean Math. Soc. 51 (2014), no. 6, 1749-1771.  https://doi.org/10.4134/BKMS.2014.51.6.1749
  9. I. K. Erken and C. Murathan, Slant Riemannian submersions from Sasakian manifolds, Arab J. Math. Sci. 22 (2016), no. 2, 250-264.  https://doi.org/10.1016/j.ajmsc.2015.12.002
  10. B. Fuglede, Harmonic morphisms between Riemannian manifolds, Annales de l'institut Fourier (Grenoble) 28 (1978), 107-144.  https://doi.org/10.5802/aif.691
  11. A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715-737. 
  12. Y. Gunduzalp, Slant submersions from almost product Riemannian manifolds, Turkish Journal of Mathematics 37 (2013), 863-873. 
  13. Y. Gunduzalp, Semi-slant submersions from almost product Riemannian manifolds, Demonstratio Mathematica 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, Turkish Journal of Mathematics 48 (2018), 2672-2689.  https://doi.org/10.3906/mat-1803-106
  15. 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
  16. T. Ishihara, A mapping of Riemannian manifolds which preserves harmonic functions, Journal of Mathematics of Kyoto University 19 (1979), 215-229. 
  17. K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. 24 (1972), 93-103. 
  18. Sumeet Kumar et al., Conformal hemi-slant submersions from almost hermitian manifolds, Commun. Korean Math. Soc. 35 (2020), no. 3, 999-1018. 
  19. M. T. Mustafa, Applications of harmonic morphisms to gravity, J. Math. Phys. 41 (2000), 6918-6929.  https://doi.org/10.1063/1.1290381
  20. B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459-469.  https://doi.org/10.1307/mmj/1028999604
  21. K. S. Park, h-slant submersions, Bull. Korean Math. Soc. 49 (2012), no. 2, 329-338.  https://doi.org/10.4134/BKMS.2012.49.2.329
  22. 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
  23. K. S. Park, H-V-semi-slant submersions from almost quaternionic Hermitian manifolds, Bull. Korean Math. Soc. 53 (2016), no. 2, 441-460.  https://doi.org/10.4134/BKMS.2016.53.2.441
  24. R. Ponge and H. Reckziegel, Twisted products in pseudo-Riemannian geometry, Geom. Dedicata 48 (1993), no. 1, 15-25.  https://doi.org/10.1007/BF01265674
  25. R. Prasad, S. S. Shukla, and S. Kumar, On quasi bi-slant submersions, Mediterr. J. Math. 16 (2019), Article Number 155. 
  26. R. Prasad and S. Pandey, Hemi-slant Riemannian maps from almost contact metric manifolds, Palestine Journal of Mathematics 9 (2020), no. 2, 811-823 
  27. R. Prasad, M. A. Akyol, P. K. Singh, and S. Kumar, On quasi bi-slant submersions from Kenmotsu manifolds onto any Riemannian manifolds, Journal of Mathematical Extension 6 (2022), no. 16, 1-25. 
  28. R. Prasad R and S. Kumar, Conformal Semi-Invariant Submersions from Almost Contact Metric Manifolds onto Riemannian Manifolds, Khayyam Journal of Mathematics 5 (2019), no. 2, 77-95. 
  29. R. Prasad, P. K. Singh, and S. Kumar, Conformal semi-slant submersions from Lorentzian para Kenmotsu manifolds, Tbilisi Mathematical Journal 14 (2021), no. 1, 191-209.  https://doi.org/10.32513/tmj/19322008115
  30. R. Prasad and S. Kumar, Conformal anti-invariant submersions from nearly Kaehler Manifolds, Palestine Journal of Mathematics 8 (2019), no. 2, 234-247. 
  31. B. Sahin, Anti-invariant Riemannian submersions from almost Hermitian manifolds, Central European J. Math. 3 (2010), 437-447.  https://doi.org/10.2478/s11533-010-0023-6
  32. B. Sahin, Semi-invariant Riemannian submersions from almost Hermitian manifolds, Canad. Math. Bull. 56 (2011), 173-183.  https://doi.org/10.4153/CMB-2011-144-8
  33. B. Sahin, Riemannian Submersions, Riemannian Maps in Hermitian Geometry and their Applications, Elsevier, Academic Press, 2017. 
  34. H. M. Tastan, B. Sahin, and S Yanan, Hemi-slant submersions, Mediterranean Journal of Mathematics 13 (2016), no. 4, 2171-2184.  https://doi.org/10.1007/s00009-015-0602-7
  35. 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, 324-349, Teubner, Leipzig, 1983.