Research Article
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Quasi-Hemi-Slant Conformal Submersions from Almost Hermitian Manifolds

Year 2021, Volume: 13 Issue: 1, 135 - 144, 30.06.2021
https://doi.org/10.47000/tjmcs.877094

Abstract

In this study, we introduce some geometric properties of quasi-hemi-slant conformal submersions from an almost Hermitian manifold to a Riemannian manifold.
We give an explicit example for this type submersions and obtain integrability conditions for certain distributions. Lastly, we search totally geodesicity
on base manifold of the map.

References

  • [1] Akyol, M.A., Conformal semi-slant submersions, Int. J. Geom. Methods Mod. Phys., 14(7)(2017), 1750114.
  • [2] Akyol, M.A., Şahin, B., Conformal anti-invariant submersions from almost Hermitian manifolds, Turk. J. Math., 40(2016), 43-70.
  • [3] Akyol, M.A., Şahin, B., Conformal semi-invariant submersions, Commun. Contemp. Math., 19(2)(2017), 1650011.
  • [4] Akyol, M.A., Şahin, B., Conformal slant submersions, Hacet. J. Math. Stat., 48(1)(2019), 28-44.
  • [5] Baird, P., Wood, J.C., Harmonic Morphism between Riemannian Manifolds, Clarendon Press, Oxford, NY, 2003.
  • [6] Falcitelli, M., Ianus, S., Pastore, A. M., Riemannian Submersions and Related Topics, World Scientific, River Edge, NJ, 2004.
  • [7] Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 16(7)(1967), 715-737.
  • [8] Kumar, S., Kumar, S., Pandey, S., Prasad, R., Conformal hemi-slant submersions from almost Hermitian manifolds, Commun. Korean Math. Soc., 35(3)(2020), 999-1018.
  • [9] Longwap, S., Massamba, F., Homti, N. E., On quasi-hemi-slant Riemannian submersion, J. Adv. Math. Comput. Sci., 34(1)(2019), 1-14.
  • [10] Miao, J., Wang, Y., Gu, X., Yau, S. T., Optimal global conformal surface parametrization for visualization, Commun. Inf. Syst., 4(2)(2005), 117-134.
  • [11] Nore, T., Second fundamental form of a map, Ann. Mat. Pur. and Appl., 146(1986), 281-310.
  • [12] O’Neill, B., The fundamental equations of a submersion, Mich. Math. J., 13(4)(1966), 459-469.
  • [13] Park, K.S., Prasad, R., Semi-slant submersions, Bull. Korean Math. Soc., 50(3)(2013), 951-962.
  • [14] Şahin, B., Horizontally conformal submersions of CR-submanifolds, Kodai Math. J., 31(1)(2008), 46-53.
  • [15] Şahin, B., Anti-invariant Riemannian submersions from almost Hermitian manifolds, Cent. Eur. J. Math., 8(3)(2010), 437-447.
  • [16] Şahin, B., Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 54(102)(1)(2011), 93-105.
  • [17] Şahin, B., Semi-invariant submersions from almost Hermitian manifolds, Can. Math. Bull., 56(1)(2013), 173-183.
  • [18] Şahin, B., Riemannian submersions from almost Hermitian manifolds, Taiwan. J. Math., 17(2)(2013), 629-659.
  • [19] Şahin, B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications, Elsevier, London, 2017.
  • [20] Taştan, H.M., Şahin, B., Yanan, S¸ ., Hemi-slant submersions, Mediterr. J. Math., 13(2016), 2171-2184.
  • [21] Wang, Y., Gu, X., Yau, S.T., Volumetric harmonic map, Commun. Inf. Syst., 3(3)(2003), 191-202.
  • [22] Wang, Y., Gu, X., Chan, T.F., Thompson, P.M., Yau, S.T., Brain surface conformal parametrization with the Ricci flow, Proceeding of the IEEE International Symposium on Biomedical Imaging-from Nano to Macro (ISBI), (2007), 1312-1315.
  • [23] Watson, B., Almost Hermitian submersions, J. Differential Geom., 11(1)(1976), 147-165.
  • [24] Yano, K., Kon, M., Structures on Manifolds, Ser. Pure Math. World Scientific, Singapore, 1984.

Year 2021, Volume: 13 Issue: 1, 135 - 144, 30.06.2021
https://doi.org/10.47000/tjmcs.877094

Abstract

References

  • [1] Akyol, M.A., Conformal semi-slant submersions, Int. J. Geom. Methods Mod. Phys., 14(7)(2017), 1750114.
  • [2] Akyol, M.A., Şahin, B., Conformal anti-invariant submersions from almost Hermitian manifolds, Turk. J. Math., 40(2016), 43-70.
  • [3] Akyol, M.A., Şahin, B., Conformal semi-invariant submersions, Commun. Contemp. Math., 19(2)(2017), 1650011.
  • [4] Akyol, M.A., Şahin, B., Conformal slant submersions, Hacet. J. Math. Stat., 48(1)(2019), 28-44.
  • [5] Baird, P., Wood, J.C., Harmonic Morphism between Riemannian Manifolds, Clarendon Press, Oxford, NY, 2003.
  • [6] Falcitelli, M., Ianus, S., Pastore, A. M., Riemannian Submersions and Related Topics, World Scientific, River Edge, NJ, 2004.
  • [7] Gray, A., Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech., 16(7)(1967), 715-737.
  • [8] Kumar, S., Kumar, S., Pandey, S., Prasad, R., Conformal hemi-slant submersions from almost Hermitian manifolds, Commun. Korean Math. Soc., 35(3)(2020), 999-1018.
  • [9] Longwap, S., Massamba, F., Homti, N. E., On quasi-hemi-slant Riemannian submersion, J. Adv. Math. Comput. Sci., 34(1)(2019), 1-14.
  • [10] Miao, J., Wang, Y., Gu, X., Yau, S. T., Optimal global conformal surface parametrization for visualization, Commun. Inf. Syst., 4(2)(2005), 117-134.
  • [11] Nore, T., Second fundamental form of a map, Ann. Mat. Pur. and Appl., 146(1986), 281-310.
  • [12] O’Neill, B., The fundamental equations of a submersion, Mich. Math. J., 13(4)(1966), 459-469.
  • [13] Park, K.S., Prasad, R., Semi-slant submersions, Bull. Korean Math. Soc., 50(3)(2013), 951-962.
  • [14] Şahin, B., Horizontally conformal submersions of CR-submanifolds, Kodai Math. J., 31(1)(2008), 46-53.
  • [15] Şahin, B., Anti-invariant Riemannian submersions from almost Hermitian manifolds, Cent. Eur. J. Math., 8(3)(2010), 437-447.
  • [16] Şahin, B., Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 54(102)(1)(2011), 93-105.
  • [17] Şahin, B., Semi-invariant submersions from almost Hermitian manifolds, Can. Math. Bull., 56(1)(2013), 173-183.
  • [18] Şahin, B., Riemannian submersions from almost Hermitian manifolds, Taiwan. J. Math., 17(2)(2013), 629-659.
  • [19] Şahin, B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications, Elsevier, London, 2017.
  • [20] Taştan, H.M., Şahin, B., Yanan, S¸ ., Hemi-slant submersions, Mediterr. J. Math., 13(2016), 2171-2184.
  • [21] Wang, Y., Gu, X., Yau, S.T., Volumetric harmonic map, Commun. Inf. Syst., 3(3)(2003), 191-202.
  • [22] Wang, Y., Gu, X., Chan, T.F., Thompson, P.M., Yau, S.T., Brain surface conformal parametrization with the Ricci flow, Proceeding of the IEEE International Symposium on Biomedical Imaging-from Nano to Macro (ISBI), (2007), 1312-1315.
  • [23] Watson, B., Almost Hermitian submersions, J. Differential Geom., 11(1)(1976), 147-165.
  • [24] Yano, K., Kon, M., Structures on Manifolds, Ser. Pure Math. World Scientific, Singapore, 1984.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Şener Yanan 0000-0003-1600-6522

Publication Date June 30, 2021
Published in Issue Year 2021 Volume: 13 Issue: 1

Cite

APA Yanan, Ş. (2021). Quasi-Hemi-Slant Conformal Submersions from Almost Hermitian Manifolds. Turkish Journal of Mathematics and Computer Science, 13(1), 135-144. https://doi.org/10.47000/tjmcs.877094
AMA Yanan Ş. Quasi-Hemi-Slant Conformal Submersions from Almost Hermitian Manifolds. TJMCS. June 2021;13(1):135-144. doi:10.47000/tjmcs.877094
Chicago Yanan, Şener. “Quasi-Hemi-Slant Conformal Submersions from Almost Hermitian Manifolds”. Turkish Journal of Mathematics and Computer Science 13, no. 1 (June 2021): 135-44. https://doi.org/10.47000/tjmcs.877094.
EndNote Yanan Ş (June 1, 2021) Quasi-Hemi-Slant Conformal Submersions from Almost Hermitian Manifolds. Turkish Journal of Mathematics and Computer Science 13 1 135–144.
IEEE Ş. Yanan, “Quasi-Hemi-Slant Conformal Submersions from Almost Hermitian Manifolds”, TJMCS, vol. 13, no. 1, pp. 135–144, 2021, doi: 10.47000/tjmcs.877094.
ISNAD Yanan, Şener. “Quasi-Hemi-Slant Conformal Submersions from Almost Hermitian Manifolds”. Turkish Journal of Mathematics and Computer Science 13/1 (June2021), 135-144. https://doi.org/10.47000/tjmcs.877094.
JAMA Yanan Ş. Quasi-Hemi-Slant Conformal Submersions from Almost Hermitian Manifolds. TJMCS. 2021;13:135–144.
MLA Yanan, Şener. “Quasi-Hemi-Slant Conformal Submersions from Almost Hermitian Manifolds”. Turkish Journal of Mathematics and Computer Science, vol. 13, no. 1, 2021, pp. 135-44, doi:10.47000/tjmcs.877094.
Vancouver Yanan Ş. Quasi-Hemi-Slant Conformal Submersions from Almost Hermitian Manifolds. TJMCS. 2021;13(1):135-44.

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