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

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

Mohd Sıddıqı Mobin Ahmad

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.

Anahtar Kelimeler

semi-Riemannian submersion, Anti-invaraint submersion

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.