Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

CONFORMAL HEMI-SLANT SUBMERSIONS FROM ALMOST HERMITIAN MANIFOLDS

  • Kumar, Sumeet (Department of Mathematics and Astronomy University of Lucknow) ;
  • Kumar, Sushil (Department of Mathematics Shri Jai Narain Post Graduate college) ;
  • Pandey, Shashikant (Department of Mathematics and Astronomy University of Lucknow) ;
  • Prasad, Rajendra (Department of Mathematics and Astronomy University of Lucknow)
  • Received : 2019.12.24
  • Accepted : 2020.05.20
  • Published : 2020.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, our main objective is to introduce the notion of conformal hemi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalized case of conformal anti-invariant submersions, conformal semi-invariant submersions and conformal slant submersions. We mainly focus on conformal hemi-slant submersions from Kähler manifolds. During this manner, we tend to study and investigate integrability of the distributions which are arisen from the definition of the submersions and the geometry of leaves of such distributions. Moreover, we tend to get necessary and sufficient conditions for these submersions to be totally geodesic for such manifolds. We also provide some quality examples of conformal hemi-slant submersions.

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 B. Sahin, Conformal semi-invariant submersions, Commun. Contemp. Math. 19 (2017), no. 2, 1650011, 22 pp. https://doi.org/10.1142/S0219199716500115
  5. M. A. Akyol and B. Sahin, Conformal slant submersions, Hacet. J. Math. Stat. 48 (2019), no. 1, 28-44. https://doi.org/10.15672/hjms.2017.506
  6. C. Altafini, Redundand robotic chains on Riemannian submersions, IEEE Transaction on Robotics and Automation 20 (2004), no. 2, 335-340. https://doi.org/10.1109/TRA.2004.824636
  7. 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. https://doi.org/10.1093/acprof:oso/9780198503620.001.0001
  8. J.-P. Bourguignon, A mathematician's visit to Kaluza-Klein theory, Rend. Sem. Mat. Univ. Politec. Torino 1989, Special Issue, 143-163 (1990).
  9. 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. http://projecteuclid.org/euclid.cmp/1103908963 https://doi.org/10.1007/BF01942061
  10. D. Chinea, Almost contact metric submersions, Rend. Circ. Mat. Palermo (2) 34 (1985), no. 1, 89-104. https://doi.org/10.1007/BF02844887
  11. U. C. De and A. A. Shaikh, Complex Manifolds and Contact Manifolds, Narosa Publishing House, New Delhi, 2009.
  12. M. Falcitelli, S. Ianus, and A. M. Pastore, Riemannian Submersions and Related Topics, World Scientific Publishing Co., Inc., River Edge, NJ, 2004. https://doi.org/10.1142/9789812562333
  13. B. Fuglede, Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble) 28 (1978), no. 2, vi, 107-144. http://www.numdam.org/item?id=AIF_1978__28_2_107_0 https://doi.org/10.5802/aif.691
  14. A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16 (1967), 715-737.
  15. S. Gundmundsson, The geometry of harmonic morphisms, Ph.D. thesis, University of Leeds, (1992).
  16. 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.
  17. Y. Gunduzalp, Slant submersions from Lorentzian almost paracontact manifolds, Gulf J. Math. 3 (2015), no. 1, 18-28.
  18. 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
  19. 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.
  20. S. Ianus and M. Visinescu, Kaluza-Klein theory with scalar fields and generalised Hopf manifolds, Classical Quantum Gravity 4 (1987), no. 5, 1317-1325. http://stacks.iop.org/0264-9381/4/1317 https://doi.org/10.1088/0264-9381/4/5/026
  21. S. Kumar, R. Prasad, and P. K. Singh, Conformal semi-slant submersions from Lorentzian para Sasakian manifolds, Commun. Korean Math. Soc. 34 (2019), no. 2, 637-655. https://doi.org/10.4134/CKMS.c180142
  22. C. Murathan and I. Kupeli Erken, Anti-invariant Riemannian submersions from cosymplectic manifolds onto Riemannian manifolds, Filomat 29 (2015), no. 7, 1429-1444. https://doi.org/10.2298/FIL1507429M
  23. B. O'Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459-469. http://projecteuclid.org/euclid.mmj/1028999604 https://doi.org/10.1307/mmj/1028999604
  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. Sahin, Anti-invariant Riemannian submersions from almost Hermitian manifolds, Cent. Eur. J. Math. 8 (2010), no. 3, 437-447. https://doi.org/10.2478/s11533-010-0023-6
  26. B. Sahin, Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 54(102) (2011), no. 1, 93-105.
  27. B. Sahin, Semi-invariant submersions from almost Hermitian manifolds, Canad. Math. Bull. 56 (2013), no. 1, 173-183. https://doi.org/10.4153/CMB-2011-144-8
  28. B. Sahin, Riemannian submersions from almost Hermitian manifolds, Taiwanese J. Math. 17 (2013), no. 2, 629-659. https://doi.org/10.11650/tjm.17.2013.2191
  29. B. Sahin, Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications, Elsevier/Academic Press, London, 2017.
  30. H. M. Tastan, B. Sahin, and Yanan, Hemi-slant submersions, Mediterr. J. Math. 13 (2016), no. 4, 2171-2184. https://doi.org/10.1007/s00009-015-0602-7
  31. B. Watson, Almost Hermitian submersions, J. Differential Geometry 11 (1976), no. 1, 147-165. http://projecteuclid.org/euclid.jdg/1214433303 https://doi.org/10.4310/jdg/1214433303
  32. B. Watson, G, G' -Riemannian submersions and nonlinear gauge field equations of general relativity, in Global analysis-analysis on manifolds, 324-349, Teubner-Texte Math., 57, Teubner, Leipzig, 1983.