Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 49 Sayı: 2, 822 - 834, 02.04.2020
https://doi.org/10.15672/hujms.458085

Öz

Kaynakça

  • [1] M.A. Akyol, Conformal semi-slant submersions, Int. J. Geom. Methods Mod. Phys. 14 (7), 2017.
  • [2] M.A. Akyol, Conformal anti-invariant submersions from cosymplectic manifolds, Hacet. J. Math. Stat. 46 (2), 177-192, 2017.
  • [3] G. Baditoiu and S. Ianus, Semi-Riemannian submersions from real and complex pseudo-hyperbolic spaces, Diff. Geom. and appl. 16, 79-84, 2002.
  • [4] J.P. Bourguignon and H.B. Lawson, A mathematician’s visit to Kaluza- Klein theory, Rend. Sem. Mat. Univ. Politec. Torino, Special Issue, 143-163, 1989.
  • [5] J.P. Bourguignon and H.B. Lawson, Stability and isolation phenomena for Yang-Mills fields, Comm. Math. Phys. 79, 189-230, 1981.
  • [6] A.V. Caldarella, On para-quaternionic submersions between para-quaternionic Kähler manifolds, Acta Applicandae Mathematicae 112, 1-14, 2010.
  • [7] P. Dacko, On almost para-cosymplectic manifolds, Tsukuba J. Math. 28 (1), 193-213, 2004.
  • [8] M. Falcitelli, S. Ianus and A. M. Pastore, Riemannian Submersions and Related Topics, World Scientific, 2004.
  • [9] Y. Gündüzalp and B. Sahin, Paracontact semi-Riemannian submersions, Turk. J.Math. 37 (1), 114-128, 2013.
  • [10] Y. Gündüzalp, B. Sahin, Para-contact para-complex semi-Riemannian submersions, Bull. Malays. Math. Sci. Soc. 37 (1), 139-152, 2014.
  • [11] Y. Gündüzalp, Anti-invariant semi-Riemannian submersions from almost para- Hermitian manifolds, J. Funct. Spaces 2013, ID 720623, 2013.
  • [12] Y. Gündüzalp, Slant submersions from almost product Riemannian manifolds, Turk. J. Math. 37, 863-873, 2013.
  • [13] Y. Gündüzalp and M.A. Akyol, Conformal slant submersions from cosymplectic manifolds, Turk. J. Math. 42 (5), 2672-2689, 2018.
  • [14] A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16, 715-737, 1967.
  • [15] S. Ianus and M. Visinescu, Kaluza-Klein theory with scalar fields and generalised Hopf manifolds, Classical Quantum Gravity 4, 1317-1352, 1987.
  • [16] S. Ianus, and M. Visinescu, Space-time compactification and Riemannian submersions, The mathematical heritage of C.F. Gauss, World Sci. Publ., River Edge, NJ, 358-371, 1991.
  • [17] S. Ianus, R. Mazzocco and G. E. Vilcu, Riemannian submersions from quaternionic manifolds, Acta Appl. Math. 104, 83-89, 2008.
  • [18] S. Ianus, G.E. Vilcu and R.C. Voicu, Harmonic maps and Riemannian submersions between manifolds endowed with special structures, Banach Center Publications 93, 277-288, 2011.
  • [19] I.K. Erken and C. Murathan, On slant Riemannian submersions for cosymplectic manifolds, Bull. Korean Math. Soc. 51 (6), 1749-1771, 2014.
  • [20] B. O‘Neill, The fundamental equations of a submersion, Michigan Math. J. 13, 459- 469, 1966.
  • [21] B. O‘Neill, Semi-Riemannian Geometry with Application to Relativity, Academic Press, New York, 1983.
  • [22] K.S.Park, H-slant submersions, Bull. Korean Math. Soc. 49, 329-338, 2012.
  • [23] B. Sahin, Slant submersions from almost Hermitian manifolds, Bull. Math. Soc.Sci. Math. Roumanie Tome. 54, 93-105, 2011.
  • [24] B.Sahin, Anti-invariant Riemannian submersions from almost Hermitian manifolds, Central European J.Math 8 (3), 437-447, 2010.
  • [25] H.M. Taştan, B.Sahin and Ş. Yanan , Hemi-slant submersions, Mediterr. J. Math. 13, 2171-2184, 2016.
  • [26] J. Welyczko, On Legendre curves in 3-dimensional normal almost paracontact metric manifolds, Results Math. 54, 377-387, 2009.
  • [27] B. Watson, Almost Hermitian submersions, J. Differential Geom. 11, 147-165, 1976.
  • [28] S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Global Anal. Geometry 36, 37-60, 2009.

Slant submersions in paracontact geometry

Yıl 2020, Cilt: 49 Sayı: 2, 822 - 834, 02.04.2020
https://doi.org/10.15672/hujms.458085

Öz

In this paper, we investigate some geometric properties of three types of slant submersions whose total space is an almost paracontact metric manifold.

Kaynakça

  • [1] M.A. Akyol, Conformal semi-slant submersions, Int. J. Geom. Methods Mod. Phys. 14 (7), 2017.
  • [2] M.A. Akyol, Conformal anti-invariant submersions from cosymplectic manifolds, Hacet. J. Math. Stat. 46 (2), 177-192, 2017.
  • [3] G. Baditoiu and S. Ianus, Semi-Riemannian submersions from real and complex pseudo-hyperbolic spaces, Diff. Geom. and appl. 16, 79-84, 2002.
  • [4] J.P. Bourguignon and H.B. Lawson, A mathematician’s visit to Kaluza- Klein theory, Rend. Sem. Mat. Univ. Politec. Torino, Special Issue, 143-163, 1989.
  • [5] J.P. Bourguignon and H.B. Lawson, Stability and isolation phenomena for Yang-Mills fields, Comm. Math. Phys. 79, 189-230, 1981.
  • [6] A.V. Caldarella, On para-quaternionic submersions between para-quaternionic Kähler manifolds, Acta Applicandae Mathematicae 112, 1-14, 2010.
  • [7] P. Dacko, On almost para-cosymplectic manifolds, Tsukuba J. Math. 28 (1), 193-213, 2004.
  • [8] M. Falcitelli, S. Ianus and A. M. Pastore, Riemannian Submersions and Related Topics, World Scientific, 2004.
  • [9] Y. Gündüzalp and B. Sahin, Paracontact semi-Riemannian submersions, Turk. J.Math. 37 (1), 114-128, 2013.
  • [10] Y. Gündüzalp, B. Sahin, Para-contact para-complex semi-Riemannian submersions, Bull. Malays. Math. Sci. Soc. 37 (1), 139-152, 2014.
  • [11] Y. Gündüzalp, Anti-invariant semi-Riemannian submersions from almost para- Hermitian manifolds, J. Funct. Spaces 2013, ID 720623, 2013.
  • [12] Y. Gündüzalp, Slant submersions from almost product Riemannian manifolds, Turk. J. Math. 37, 863-873, 2013.
  • [13] Y. Gündüzalp and M.A. Akyol, Conformal slant submersions from cosymplectic manifolds, Turk. J. Math. 42 (5), 2672-2689, 2018.
  • [14] A. Gray, Pseudo-Riemannian almost product manifolds and submersions, J. Math. Mech. 16, 715-737, 1967.
  • [15] S. Ianus and M. Visinescu, Kaluza-Klein theory with scalar fields and generalised Hopf manifolds, Classical Quantum Gravity 4, 1317-1352, 1987.
  • [16] S. Ianus, and M. Visinescu, Space-time compactification and Riemannian submersions, The mathematical heritage of C.F. Gauss, World Sci. Publ., River Edge, NJ, 358-371, 1991.
  • [17] S. Ianus, R. Mazzocco and G. E. Vilcu, Riemannian submersions from quaternionic manifolds, Acta Appl. Math. 104, 83-89, 2008.
  • [18] S. Ianus, G.E. Vilcu and R.C. Voicu, Harmonic maps and Riemannian submersions between manifolds endowed with special structures, Banach Center Publications 93, 277-288, 2011.
  • [19] I.K. Erken and C. Murathan, On slant Riemannian submersions for cosymplectic manifolds, Bull. Korean Math. Soc. 51 (6), 1749-1771, 2014.
  • [20] B. O‘Neill, The fundamental equations of a submersion, Michigan Math. J. 13, 459- 469, 1966.
  • [21] B. O‘Neill, Semi-Riemannian Geometry with Application to Relativity, Academic Press, New York, 1983.
  • [22] K.S.Park, H-slant submersions, Bull. Korean Math. Soc. 49, 329-338, 2012.
  • [23] B. Sahin, Slant submersions from almost Hermitian manifolds, Bull. Math. Soc.Sci. Math. Roumanie Tome. 54, 93-105, 2011.
  • [24] B.Sahin, Anti-invariant Riemannian submersions from almost Hermitian manifolds, Central European J.Math 8 (3), 437-447, 2010.
  • [25] H.M. Taştan, B.Sahin and Ş. Yanan , Hemi-slant submersions, Mediterr. J. Math. 13, 2171-2184, 2016.
  • [26] J. Welyczko, On Legendre curves in 3-dimensional normal almost paracontact metric manifolds, Results Math. 54, 377-387, 2009.
  • [27] B. Watson, Almost Hermitian submersions, J. Differential Geom. 11, 147-165, 1976.
  • [28] S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Global Anal. Geometry 36, 37-60, 2009.
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Yılmaz Gündüzalp 0000-0002-0932-949X

Yayımlanma Tarihi 2 Nisan 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 49 Sayı: 2

Kaynak Göster

APA Gündüzalp, Y. (2020). Slant submersions in paracontact geometry. Hacettepe Journal of Mathematics and Statistics, 49(2), 822-834. https://doi.org/10.15672/hujms.458085
AMA Gündüzalp Y. Slant submersions in paracontact geometry. Hacettepe Journal of Mathematics and Statistics. Nisan 2020;49(2):822-834. doi:10.15672/hujms.458085
Chicago Gündüzalp, Yılmaz. “Slant Submersions in Paracontact Geometry”. Hacettepe Journal of Mathematics and Statistics 49, sy. 2 (Nisan 2020): 822-34. https://doi.org/10.15672/hujms.458085.
EndNote Gündüzalp Y (01 Nisan 2020) Slant submersions in paracontact geometry. Hacettepe Journal of Mathematics and Statistics 49 2 822–834.
IEEE Y. Gündüzalp, “Slant submersions in paracontact geometry”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 2, ss. 822–834, 2020, doi: 10.15672/hujms.458085.
ISNAD Gündüzalp, Yılmaz. “Slant Submersions in Paracontact Geometry”. Hacettepe Journal of Mathematics and Statistics 49/2 (Nisan 2020), 822-834. https://doi.org/10.15672/hujms.458085.
JAMA Gündüzalp Y. Slant submersions in paracontact geometry. Hacettepe Journal of Mathematics and Statistics. 2020;49:822–834.
MLA Gündüzalp, Yılmaz. “Slant Submersions in Paracontact Geometry”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 2, 2020, ss. 822-34, doi:10.15672/hujms.458085.
Vancouver Gündüzalp Y. Slant submersions in paracontact geometry. Hacettepe Journal of Mathematics and Statistics. 2020;49(2):822-34.