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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 Articles
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 (June 2021), 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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