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Conformal Quasi-Hemi-Slant Riemannian Maps

Yıl 2022, Cilt: 5 Sayı: 2, 99 - 113, 30.06.2022

Şener Yanan

https://doi.org/10.33434/cams.1084830

Öz

In this paper, we state some geometric properties of conformal quasi-hemi-slant Riemannian maps from almost Hermitian manifolds to Riemannian manifolds. We give necessary and sufficient conditions for certain distributions to be integrable and get examples. For such distributions, we examine which conditions define totally geodesic foliations on base manifold. In addition, we apply notion of pluriharmonicity to get some relations between horizontally homothetic maps and conformal quasi-hemi-slant Riemannian maps.

Anahtar Kelimeler

Riemannian map conformal Riemannian map conformal quasi-hemi-slant Riemannian map

Kaynakça

  • [1] M. A. Akyol, Conformal semi-slant submersions, Int. J. Geom, 14(7) (2017), 1750114.
  • [2] M. A. Akyol, B. S¸ ahin, Conformal anti-invariant submersions from almost Hermitian manifolds, Turk. J. Math., 40(1) (2016), 43-70.
  • [3] M. A. Akyol, B. S¸ ahin, Conformal semi-invariant submersions, Commun. Contemp. Math., 19(2) (2017), 1650011.
  • [4] M. A. Akyol, B. S¸ ahin, Conformal slant submersions, Hacettepe J. Math. Stat., 48(1) (2019), 28-44.
  • [5] P. Baird, J. C. Wood, Harmonic Morphism between Riemannian Manifolds, Clarendon Press, Oxford, 2003.
  • [6] B. Y. Chen, Riemannian Submanifolds. Handbook of Differential Geometry, North-Holland, Amsterdam, 2000.
  • [7] M. Falcitelli, S. Ianus, A. M. Pastore, Riemannian submersions and related topics, World Scientific, NJ, 2004.
  • [8] A. E. Fischer, Riemannian maps between Riemannian manifolds, Contemp. Math., 132 (1992), 331-366.
  • [9] E. Garcia-Rio, D. N. Kupeli, Semi-Riemannian Maps and Their Applications, Kluwer Academic, Dordrecht, 1999.
  • [10] A. Gray, Pseudo-Riemannian almost product manifolds and submersions, Appl. Math. Mech., 16(7) (1967), 715-737.
  • [11] S. Kumar, S. Kumar, S. Pandey, R. Prasad, Conformal hemi-slant submersions from almost Hermitian manifolds, Commun. Korean Math. Soc., 35(3) (2020), 999-1018.
  • [12] C.W. Lee, J.W. Lee, B. S¸ ahin, G. Vilcu, Optimal inequalities for Riemannian maps and Riemannian submersions involving Casorati curvatures, Ann. di Mat. Pura ed Appl., 200(3) (2021), 1277-1295.
  • [13] S. Longwap, F. Massamba, N. E. Homti, On quasi-hemi-slant Riemannian submersion, JAMCS, 34(1) (2019), 1-14.
  • [14] J. Miao, Y. Wang, X. Gu, S. T. Yau, Optimal global conformal surface parametrization for visualization, Comm. Inf. Sys., 4(2) (2005), 117-134.
  • [15] T. Nore, Second fundamental form of a map, Ann. di Mat. Pura ed Appl., 146 (1986), 281-310.
  • [16] Y. Ohnita, On pluriharmonicity of stable harmonic maps, J. London Math. Soc., s2-35(3) (1987), 563-587.
  • [17] B. O’Neill, The fundamental equations of a submersion, Mich. Math. J., 13(4) (1966), 459-469.
  • [18] K. S. Park, Semi-slant Riemannian map, Quaest. Math., 41(1) (2018), 1-14.
  • [19] R. Prasad, S. Kumar, S. Kumar, A. Turgut Vanlı, On quasi-hemi-slant Riemannian maps, Gazi Univ. J. Sci., 34(2) (2021), 477-491.
  • [20] B. S¸ ahin, Generic Riemannian maps, Miskolc Math. Notes, 18(1) (2017), 453-467.
  • [21] B. S¸ ahin, Semi-invariant Riemannian maps from almost Hermitian manifolds, Indag. Math., 23(1) (2012), 80-94.
  • [22] B. S¸ ahin, Slant Riemannian maps from almost Hermitian manifolds, Quaest. Math., 36(3) (2013), 449-461.
  • [23] B. S¸ ahin, Hemi-slant Riemannian maps, Mediterr. J. Math., 14 Article number:10 (2017).
  • [24] B. S¸ ahin, Conformal Riemannian maps between Riemannian manifolds, their harmonicity and decomposition theorems, Acta Appl. Math., 109 (2010), 829-847.
  • [25] B. S¸ ahin, Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications, Elsevier, London, 2017.
  • [26] B. S¸ ahin, S¸ . Yanan, Conformal Riemannian maps from almost Hermitian manifolds, Turk. J. Math., 42(5) (2018), 2436- 2451.
  • [27] B. S¸ ahin, S¸ . Yanan, Conformal semi-invariant Riemannian maps from almost Hermitian manifolds, Filomat, 33(4) (2019), 1125-1134.
  • [28] Y. Wang, X. Gu, S. T. Yau, Volumetric harmonic map, Comm. Inf. Sys., 3(3) (2003), 191-202.
  • [29] Y. Wang, X. Gu, T. F. Chan, P. M. Thompson, S. T. Yau, 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.
  • [30] B. Watson, Almost Hermitian submersions, J. Differ. Geom., 11 (1976), 147-165.
  • [31] S¸ . Yanan, Quasi-hemi-slant conformal submersions from almost Hermitian manifolds, Turk. J. Math. Comput. Sci., 13(1) (2021), 135-144.
  • [32] S¸ . Yanan, Conformal generic Riemannian maps from almost Hermitian manifolds, Turk. J. Sci., 6(2) (2021), 76-88.
  • [33] S¸ . Yanan, Conformal hemi-slant Riemannian maps, FCMS, 3(1) (2022), 57-74.
  • [34] S¸ . Yanan, Conformal semi-slant Riemannian maps from almost Hermitian manifolds onto Riemannian manifolds, Filomat, 36(5) (2022).
  • [35] S¸ . Yanan, B. S¸ ahin, Conformal slant Riemannian maps, Int. J. Maps Math., 5(1) (2022), 78-100.
  • [36] K. Yano, M. Kon, Structures on Manifolds, World Scientific, Singapore, 1984.

Yıl 2022, Cilt: 5 Sayı: 2, 99 - 113, 30.06.2022

Şener Yanan

https://doi.org/10.33434/cams.1084830

Öz

Kaynakça

  • [1] M. A. Akyol, Conformal semi-slant submersions, Int. J. Geom, 14(7) (2017), 1750114.
  • [2] M. A. Akyol, B. S¸ ahin, Conformal anti-invariant submersions from almost Hermitian manifolds, Turk. J. Math., 40(1) (2016), 43-70.
  • [3] M. A. Akyol, B. S¸ ahin, Conformal semi-invariant submersions, Commun. Contemp. Math., 19(2) (2017), 1650011.
  • [4] M. A. Akyol, B. S¸ ahin, Conformal slant submersions, Hacettepe J. Math. Stat., 48(1) (2019), 28-44.
  • [5] P. Baird, J. C. Wood, Harmonic Morphism between Riemannian Manifolds, Clarendon Press, Oxford, 2003.
  • [6] B. Y. Chen, Riemannian Submanifolds. Handbook of Differential Geometry, North-Holland, Amsterdam, 2000.
  • [7] M. Falcitelli, S. Ianus, A. M. Pastore, Riemannian submersions and related topics, World Scientific, NJ, 2004.
  • [8] A. E. Fischer, Riemannian maps between Riemannian manifolds, Contemp. Math., 132 (1992), 331-366.
  • [9] E. Garcia-Rio, D. N. Kupeli, Semi-Riemannian Maps and Their Applications, Kluwer Academic, Dordrecht, 1999.
  • [10] A. Gray, Pseudo-Riemannian almost product manifolds and submersions, Appl. Math. Mech., 16(7) (1967), 715-737.
  • [11] S. Kumar, S. Kumar, S. Pandey, R. Prasad, Conformal hemi-slant submersions from almost Hermitian manifolds, Commun. Korean Math. Soc., 35(3) (2020), 999-1018.
  • [12] C.W. Lee, J.W. Lee, B. S¸ ahin, G. Vilcu, Optimal inequalities for Riemannian maps and Riemannian submersions involving Casorati curvatures, Ann. di Mat. Pura ed Appl., 200(3) (2021), 1277-1295.
  • [13] S. Longwap, F. Massamba, N. E. Homti, On quasi-hemi-slant Riemannian submersion, JAMCS, 34(1) (2019), 1-14.
  • [14] J. Miao, Y. Wang, X. Gu, S. T. Yau, Optimal global conformal surface parametrization for visualization, Comm. Inf. Sys., 4(2) (2005), 117-134.
  • [15] T. Nore, Second fundamental form of a map, Ann. di Mat. Pura ed Appl., 146 (1986), 281-310.
  • [16] Y. Ohnita, On pluriharmonicity of stable harmonic maps, J. London Math. Soc., s2-35(3) (1987), 563-587.
  • [17] B. O’Neill, The fundamental equations of a submersion, Mich. Math. J., 13(4) (1966), 459-469.
  • [18] K. S. Park, Semi-slant Riemannian map, Quaest. Math., 41(1) (2018), 1-14.
  • [19] R. Prasad, S. Kumar, S. Kumar, A. Turgut Vanlı, On quasi-hemi-slant Riemannian maps, Gazi Univ. J. Sci., 34(2) (2021), 477-491.
  • [20] B. S¸ ahin, Generic Riemannian maps, Miskolc Math. Notes, 18(1) (2017), 453-467.
  • [21] B. S¸ ahin, Semi-invariant Riemannian maps from almost Hermitian manifolds, Indag. Math., 23(1) (2012), 80-94.
  • [22] B. S¸ ahin, Slant Riemannian maps from almost Hermitian manifolds, Quaest. Math., 36(3) (2013), 449-461.
  • [23] B. S¸ ahin, Hemi-slant Riemannian maps, Mediterr. J. Math., 14 Article number:10 (2017).
  • [24] B. S¸ ahin, Conformal Riemannian maps between Riemannian manifolds, their harmonicity and decomposition theorems, Acta Appl. Math., 109 (2010), 829-847.
  • [25] B. S¸ ahin, Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications, Elsevier, London, 2017.
  • [26] B. S¸ ahin, S¸ . Yanan, Conformal Riemannian maps from almost Hermitian manifolds, Turk. J. Math., 42(5) (2018), 2436- 2451.
  • [27] B. S¸ ahin, S¸ . Yanan, Conformal semi-invariant Riemannian maps from almost Hermitian manifolds, Filomat, 33(4) (2019), 1125-1134.
  • [28] Y. Wang, X. Gu, S. T. Yau, Volumetric harmonic map, Comm. Inf. Sys., 3(3) (2003), 191-202.
  • [29] Y. Wang, X. Gu, T. F. Chan, P. M. Thompson, S. T. Yau, 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.
  • [30] B. Watson, Almost Hermitian submersions, J. Differ. Geom., 11 (1976), 147-165.
  • [31] S¸ . Yanan, Quasi-hemi-slant conformal submersions from almost Hermitian manifolds, Turk. J. Math. Comput. Sci., 13(1) (2021), 135-144.
  • [32] S¸ . Yanan, Conformal generic Riemannian maps from almost Hermitian manifolds, Turk. J. Sci., 6(2) (2021), 76-88.
  • [33] S¸ . Yanan, Conformal hemi-slant Riemannian maps, FCMS, 3(1) (2022), 57-74.
  • [34] S¸ . Yanan, Conformal semi-slant Riemannian maps from almost Hermitian manifolds onto Riemannian manifolds, Filomat, 36(5) (2022).
  • [35] S¸ . Yanan, B. S¸ ahin, Conformal slant Riemannian maps, Int. J. Maps Math., 5(1) (2022), 78-100.
  • [36] K. Yano, M. Kon, Structures on Manifolds, World Scientific, Singapore, 1984.
Toplam 36 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Şener Yanan 0000-0003-1600-6522

Yayımlanma Tarihi 30 Haziran 2022
Gönderilme Tarihi 8 Mart 2022
Kabul Tarihi 7 Haziran 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: 2

Kaynak Göster

APA Yanan, Ş. (2022). Conformal Quasi-Hemi-Slant Riemannian Maps. Communications in Advanced Mathematical Sciences, 5(2), 99-113. https://doi.org/10.33434/cams.1084830
AMA Yanan Ş. Conformal Quasi-Hemi-Slant Riemannian Maps. Communications in Advanced Mathematical Sciences. Haziran 2022;5(2):99-113. doi:10.33434/cams.1084830
Chicago Yanan, Şener. “Conformal Quasi-Hemi-Slant Riemannian Maps”. Communications in Advanced Mathematical Sciences 5, sy. 2 (Haziran 2022): 99-113. https://doi.org/10.33434/cams.1084830.
EndNote Yanan Ş (01 Haziran 2022) Conformal Quasi-Hemi-Slant Riemannian Maps. Communications in Advanced Mathematical Sciences 5 2 99–113.
IEEE Ş. Yanan, “Conformal Quasi-Hemi-Slant Riemannian Maps”, Communications in Advanced Mathematical Sciences, c. 5, sy. 2, ss. 99–113, 2022, doi: 10.33434/cams.1084830.
ISNAD Yanan, Şener. “Conformal Quasi-Hemi-Slant Riemannian Maps”. Communications in Advanced Mathematical Sciences 5/2 (Haziran 2022), 99-113. https://doi.org/10.33434/cams.1084830.
JAMA Yanan Ş. Conformal Quasi-Hemi-Slant Riemannian Maps. Communications in Advanced Mathematical Sciences. 2022;5:99–113.
MLA Yanan, Şener. “Conformal Quasi-Hemi-Slant Riemannian Maps”. Communications in Advanced Mathematical Sciences, c. 5, sy. 2, 2022, ss. 99-113, doi:10.33434/cams.1084830.
Vancouver Yanan Ş. Conformal Quasi-Hemi-Slant Riemannian Maps. Communications in Advanced Mathematical Sciences. 2022;5(2):99-113.
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