Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2020, Cilt: 8 Sayı: 1, 38 - 49, 15.04.2020

Öz

Kaynakça

  • [1] A. Gray, Pseudo-Riemannian almost product manifolds and submersion, J. Math. Mech., 16 (1967) 715-737.
  • [2] B. Watson, Almost Hermitian submersions, J. Differential Geom. (1)(1976) 147-165.
  • [3] B. O’Neill, The fundamental equations of a submersion, Mich. Math. J. 13(1966) 458-469.
  • [4] B. O’Neill. Semi-Riemannian geometry, volume 103 of Pure and Applied Mathematics. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. With applications to relativity.
  • [5] B.S. ahin, Anti-invariant Riemannian submersions from almost Hermitian manifolds, Cent. Eur. J. Math.8(3)(2010) 437-447.
  • [6] B.S. ahin, Semi-invariant submersions from almost Hermitian manifolds, Canadian. Math. Bull.(1)(2013) 173-182.
  • [7] B.S. ahin, Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie 54(102)(2011) No. 1, 93-105.
  • [8] C. Chinea, Almost contact metric submersions, Rend. Circ. Mat. Palermo, 43(1), 89-104, 1985.
  • [9] E. Garcia-Rio and D. N. Kupeli. Semi-Riemannian maps and their applications, volume 475 of Mathematics and its Applications. Kluwer Academic Publishers, Dordrecht, 1999.
  • [10] Gray, A. and Hervella, L.M., The sixteen class of almost Hermitian manifolds and their linear invariants, Ann. Math. Pura Appl.,16 ( 1967 ) 715-737.
  • [11] H. M. Tas¸tan, On Lagrangian submersions, Hacettepe J. Math. Stat. 43 (46) (2014) 993-1000.
  • [12] J. W. Lee, Anti-invariant x?􀀀 Riemannian submersions from almost contact manifolds, Hacettepe J. Math. Stat. 42(2), 231-241, 2013.
  • [13] J. P. Bourguignon and H. B. Lawson, Jr. Stability and isolation phenomena for Yang- Mills fields. Comm. Math. Phys., 79(2):189230, 1981.
  • [14] J. P. Bourguignon. A mathematician’s visit to Kaluza-Klein theory. Rend. Sem. Mat. Univ. Politec. Torino, pages 143163 (1990), 1989. Conference on Partial Differential Equations and Geometry (Torino, 1988).
  • [15] M. D. Siddiqi, M. A. Akyol., Anti-invariant xRiemannian Submersions from hyperbolic b-Kenmotsu Manifolds, CUBO A Mathematical Journal, 20 (1), 79-94, 2018.
  • [16] M. A. Akyol, Conformal anti-invariant submersions from cosymplectic manifolds,Hacet. J. Math. Stat.(2016), Doi: 10.15672/HJMS.20174720336.
  • [17] M. A. Akyol, R. Sari., E. Aksoy., Semi-invariant x?-Riemannian submersions from almost contact metric manifolds, Int. J. Geometric Methods in Modern Physics Vol. 14, No. 5 (2017) 1750074 (17pages).
  • [18] M. D. Siddiqi, M. A. Akyol., Anti-invariant x?􀀀 Riemannian Submersions from almost hyperbolic contact Manifolds, Int. Electronic J. Geometry, 12(1), (2019), 32-42.
  • [19] M. A. Akyol and Y. Gunduzlap., Semi-invariant semi-Riemannian submersions, Commu. Fac. Sci. Univ. Ank. Series A, 67(1), (2018),32-42.
  • [20] M. Faghfouri, S. Mashmouli, On anti-invariant semi-Riemannian submersions from Lorentzian (para) Sasakian manifolds, arXiv: 1702.02409v4 [math.DG] 30 Aug 2017.
  • [21] M. Falcitelli, S. Ianus and A.M. Pastore, Riemannian submersions and related topics (World Scientific, River Edge, NJ, 2004.
  • [22] M. Falcitelli, A. M. Pastore, A note on almost K¨ahler and nearly K¨ahler submersions, J. Geom. 69( 2000) 79-87.
  • [23] Oubina, J.A. New classes of almost contact metric structures, Pub. Math. Debrecen,f32 (1980) 187-193.
  • [24] P. Baird , J.C. Wood, Harmonic morphism between Riemannian manifolds, Oxford science publications, 2003.
  • [25] S. Ianus and M. Visinescu. Kaluza-Klein theory with scalar fields and generalized Hopf manifolds. Classical Quantum Gravity, 4(5):13171325, 1987.
  • [26] S. Ianus and M. Visinescu., Space-time compactification and Riemannian submersions. In The mathematical heritage of C. F. Gauss, pages 358-371. World Sci. Publ., River Edge, NJ, 1991.
  • [27] S. Kaneyuki, F. L. Williams., Almost paracontact and prahodge staructures on manifolds. Nagoya Math. J. 99 (1985), 173-187.
  • [28] Y. I. Gunduzlap., Sahin, B., Paracontact para-complex semi-Riemannian submersions, Bull. Malays. Math. Sci. Soc. (2) 37(1), (2014), 139-152.

Anti-Invariant Semi-Riemannian Submersions from Indefinite Almost Contact Metric Manifolds

Yıl 2020, Cilt: 8 Sayı: 1, 38 - 49, 15.04.2020

Öz

In this paper, we study an anti-invariant semi-Riemmannian submersions from indefinite almost contact metric manifolds. We obtain, the necessary and sufficient conditions for the characteristics vector filed to be vertical and horizontal. aMoreover, we find the conditions of integrability and hormonicness of this submersion map. Finally, we furnish an example of an anti-invariant semi-Riemannian submersion from indefinite almost contact metric manifold which is indefinite trans-Sasakian manifolds in the present paper.

Kaynakça

  • [1] A. Gray, Pseudo-Riemannian almost product manifolds and submersion, J. Math. Mech., 16 (1967) 715-737.
  • [2] B. Watson, Almost Hermitian submersions, J. Differential Geom. (1)(1976) 147-165.
  • [3] B. O’Neill, The fundamental equations of a submersion, Mich. Math. J. 13(1966) 458-469.
  • [4] B. O’Neill. Semi-Riemannian geometry, volume 103 of Pure and Applied Mathematics. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. With applications to relativity.
  • [5] B.S. ahin, Anti-invariant Riemannian submersions from almost Hermitian manifolds, Cent. Eur. J. Math.8(3)(2010) 437-447.
  • [6] B.S. ahin, Semi-invariant submersions from almost Hermitian manifolds, Canadian. Math. Bull.(1)(2013) 173-182.
  • [7] B.S. ahin, Slant submersions from almost Hermitian manifolds, Bull. Math. Soc. Sci. Math. Roumanie 54(102)(2011) No. 1, 93-105.
  • [8] C. Chinea, Almost contact metric submersions, Rend. Circ. Mat. Palermo, 43(1), 89-104, 1985.
  • [9] E. Garcia-Rio and D. N. Kupeli. Semi-Riemannian maps and their applications, volume 475 of Mathematics and its Applications. Kluwer Academic Publishers, Dordrecht, 1999.
  • [10] Gray, A. and Hervella, L.M., The sixteen class of almost Hermitian manifolds and their linear invariants, Ann. Math. Pura Appl.,16 ( 1967 ) 715-737.
  • [11] H. M. Tas¸tan, On Lagrangian submersions, Hacettepe J. Math. Stat. 43 (46) (2014) 993-1000.
  • [12] J. W. Lee, Anti-invariant x?􀀀 Riemannian submersions from almost contact manifolds, Hacettepe J. Math. Stat. 42(2), 231-241, 2013.
  • [13] J. P. Bourguignon and H. B. Lawson, Jr. Stability and isolation phenomena for Yang- Mills fields. Comm. Math. Phys., 79(2):189230, 1981.
  • [14] J. P. Bourguignon. A mathematician’s visit to Kaluza-Klein theory. Rend. Sem. Mat. Univ. Politec. Torino, pages 143163 (1990), 1989. Conference on Partial Differential Equations and Geometry (Torino, 1988).
  • [15] M. D. Siddiqi, M. A. Akyol., Anti-invariant xRiemannian Submersions from hyperbolic b-Kenmotsu Manifolds, CUBO A Mathematical Journal, 20 (1), 79-94, 2018.
  • [16] M. A. Akyol, Conformal anti-invariant submersions from cosymplectic manifolds,Hacet. J. Math. Stat.(2016), Doi: 10.15672/HJMS.20174720336.
  • [17] M. A. Akyol, R. Sari., E. Aksoy., Semi-invariant x?-Riemannian submersions from almost contact metric manifolds, Int. J. Geometric Methods in Modern Physics Vol. 14, No. 5 (2017) 1750074 (17pages).
  • [18] M. D. Siddiqi, M. A. Akyol., Anti-invariant x?􀀀 Riemannian Submersions from almost hyperbolic contact Manifolds, Int. Electronic J. Geometry, 12(1), (2019), 32-42.
  • [19] M. A. Akyol and Y. Gunduzlap., Semi-invariant semi-Riemannian submersions, Commu. Fac. Sci. Univ. Ank. Series A, 67(1), (2018),32-42.
  • [20] M. Faghfouri, S. Mashmouli, On anti-invariant semi-Riemannian submersions from Lorentzian (para) Sasakian manifolds, arXiv: 1702.02409v4 [math.DG] 30 Aug 2017.
  • [21] M. Falcitelli, S. Ianus and A.M. Pastore, Riemannian submersions and related topics (World Scientific, River Edge, NJ, 2004.
  • [22] M. Falcitelli, A. M. Pastore, A note on almost K¨ahler and nearly K¨ahler submersions, J. Geom. 69( 2000) 79-87.
  • [23] Oubina, J.A. New classes of almost contact metric structures, Pub. Math. Debrecen,f32 (1980) 187-193.
  • [24] P. Baird , J.C. Wood, Harmonic morphism between Riemannian manifolds, Oxford science publications, 2003.
  • [25] S. Ianus and M. Visinescu. Kaluza-Klein theory with scalar fields and generalized Hopf manifolds. Classical Quantum Gravity, 4(5):13171325, 1987.
  • [26] S. Ianus and M. Visinescu., Space-time compactification and Riemannian submersions. In The mathematical heritage of C. F. Gauss, pages 358-371. World Sci. Publ., River Edge, NJ, 1991.
  • [27] S. Kaneyuki, F. L. Williams., Almost paracontact and prahodge staructures on manifolds. Nagoya Math. J. 99 (1985), 173-187.
  • [28] Y. I. Gunduzlap., Sahin, B., Paracontact para-complex semi-Riemannian submersions, Bull. Malays. Math. Sci. Soc. (2) 37(1), (2014), 139-152.
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Mohd Sıddıqı 0000-0002-1713-6831

Mobin Ahmad Bu kişi benim

Yayımlanma Tarihi 15 Nisan 2020
Gönderilme Tarihi 9 Şubat 2019
Kabul Tarihi 17 Şubat 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 8 Sayı: 1

Kaynak Göster

APA Sıddıqı, M., & Ahmad, M. (2020). Anti-Invariant Semi-Riemannian Submersions from Indefinite Almost Contact Metric Manifolds. Konuralp Journal of Mathematics, 8(1), 38-49.
AMA Sıddıqı M, Ahmad M. Anti-Invariant Semi-Riemannian Submersions from Indefinite Almost Contact Metric Manifolds. Konuralp J. Math. Nisan 2020;8(1):38-49.
Chicago Sıddıqı, Mohd, ve Mobin Ahmad. “Anti-Invariant Semi-Riemannian Submersions from Indefinite Almost Contact Metric Manifolds”. Konuralp Journal of Mathematics 8, sy. 1 (Nisan 2020): 38-49.
EndNote Sıddıqı M, Ahmad M (01 Nisan 2020) Anti-Invariant Semi-Riemannian Submersions from Indefinite Almost Contact Metric Manifolds. Konuralp Journal of Mathematics 8 1 38–49.
IEEE M. Sıddıqı ve M. Ahmad, “Anti-Invariant Semi-Riemannian Submersions from Indefinite Almost Contact Metric Manifolds”, Konuralp J. Math., c. 8, sy. 1, ss. 38–49, 2020.
ISNAD Sıddıqı, Mohd - Ahmad, Mobin. “Anti-Invariant Semi-Riemannian Submersions from Indefinite Almost Contact Metric Manifolds”. Konuralp Journal of Mathematics 8/1 (Nisan 2020), 38-49.
JAMA Sıddıqı M, Ahmad M. Anti-Invariant Semi-Riemannian Submersions from Indefinite Almost Contact Metric Manifolds. Konuralp J. Math. 2020;8:38–49.
MLA Sıddıqı, Mohd ve Mobin Ahmad. “Anti-Invariant Semi-Riemannian Submersions from Indefinite Almost Contact Metric Manifolds”. Konuralp Journal of Mathematics, c. 8, sy. 1, 2020, ss. 38-49.
Vancouver Sıddıqı M, Ahmad M. Anti-Invariant Semi-Riemannian Submersions from Indefinite Almost Contact Metric Manifolds. Konuralp J. Math. 2020;8(1):38-49.
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