Semi-Invariant Riemannian Submersions with Semi-Symmetric Non-Metric Connection

Yıl 2021, Sayı: 35, 62 - 71, 30.06.2021

Ramazan Sarı

https://doi.org/10.53570/jnt.904708

Öz

In this paper, we investigate semi-invariant Riemannian submersion from a Kaehler manifold with semi-symmetric non-metric connection to a Riemannian manifold. We study the geometry of foliations with semi-symmetric non-metric connection. Later, we introduce base manifold to be a local product manifold with semi-symmetric non-metric connection.

Anahtar Kelimeler

Riemannian submersions, semi-invariant submersions, semi-symmetric non-metric connection, Kaehler manifold

Kaynakça

• B. O'Neill, The Fundamental Equations of a Submersion, Michigan Mathematics Journal 13 (1966) 458-469.
• A. Gray, Pseudo-Riemannian Almost Product Manifolds and Submersions, Journal of Mathematics and Mechanics 16 (1967) 715-737.
• M. A. Akyol, G. Ayar, New Curvature Tensors Along Riemannian Submersion, Arxiv:2007.07814v1.
• M. A. Akyol, Conformal Semi-Slant Submersions, International Journal of Geometric Methods in Modern Physics 14(7) (2017) 1750114.
• M. A. Akyol, R. Sarı, Semi Slant $ξ^⊥$-Riemannian Submersion, Mediterranean Journal of Mathematics 14 (2017) Article No. 234.
• K. S. Park, R. Prasad, Semi-Slant Submersions, Bulletin Korean Mathematical Society 50(3) (2013) 951-962.
• M. A. Akyol, Y. Gündüzalp, Hemi-Slant Submersions from Almost Product Riemannian Manifolds, Gulf Journal of Mathematics 4(3) (2016) 15-27.
• R. Sarı, M. Akyol, Hemi-Slant $ξ^⊥$-Riemannian Submersions in Contact Geometry, Filomat 34(11) (2020) 3747-3758.
• H. M. Taştan, B. Şahin, Ş. Yanan, Hemi-Slant Submersions, Mediterranean Journal of Mathematics 13(4) (2016) 2171-2184.
• M. A. Akyol, R. Sarı, E. Aksoy, Semi-Invariant $ξ^⊥$-Riemannian Submersions from Almost Contact Metric Manifolds, International Journal of Geometric Methods in Modern Physics 14 (2017) 1750074.
• K. S. Park, H-Semi-Invariant Submersions, Taiwanese Journal of Mathematics 16 (2012) 5 1865-1878.
• B. Şahin, Semi-Invariant Riemannian Submersions from Almost Hermitian Manifolds, Canadian Mathematical Bulletin 56 (2011) 173-183.
• S. Ali, T. Fatima, Anti-Invariant Riemannian Submersions from Nearly Kaehler Manifolds, Filomat 27(7) (2013) 1219-1235.
• J. W. Lee, Anti-invariant $ξ^⊥$-Riemannian Submersions from Almost Contact Manifolds, Hacettepe Journal of Mathematics and Statistics 42(3) (2013) 231-241.
• B. Şahin, Anti-invariant Riemannian submersions from almost Hermitian manifolds, Central European Journal of Mathematics 3 (2010) 437-447.
• A. Friedmann, J. A. Schouten, Uber die Geometrie der Halbsymmetrischen Ubertragungen, Math Zeitschrift, 21 (1924) 211-233.
• H. A. Hayden, Subspaces of a Space with Torsion, Proceedings of the London Mathematical Society 34 (1932) 27-50.
• K. Yano, On Semi-Symmetric Metric Connection, Revue Roumaine de Mathematiques Pures et Appliquees 15 (1970) 1579-1586.
• N. S. Agashe, M. R. Chafle, A Semi-Symmetric Non-Metric Connection on a Riemannian Manifold, Indian Journal of Pure and Applied Mathematics 23(6) (1992) 399-409.
• G. Ayar, D. Demirhan, Ricci Solition on Nearly Kenmotsu Manifolds with Semi-Symmetric Metric Connection, Journal of Engineering Technology and Applied Sciences 4(3) (2019) 131-140.
• M. Altın, Projective Curvature N(k) Contact Metric Manifold Admitting Semi-Symetric Non-Metric Connection, Fundamental Journal of Mathematics and Applications 3(2) (2020) 94-100.
• M. A. Akyol, R. Sarı, On CR-Submanifolds of a S-Manifold Endowed with a Semi-Symmetric non-Metric Connection, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 65(1) (2016) 171-185.
• R. Sarı, M. Akyol, E. Aksoy Sarı, Some Properties of CR-Submanifolds of an S-Manifold with a Semi-Symmetric Metric Connection, Celal Bayar University Journal of Science 13(3) (2017) 729-736.
• A. T. Vanlı, İ. Ünal, D. Özdemir, Normal Complex Contact Metric Manifolds Admitting a Semi Symmetric Metric Connection, Applied Mathematics and Nonlinear Sciences 5(2) (2020) 49-66.
• A. T. Vanlı, R. Sarı, On Semi-Invariant Submanifold of a Generalized Kenmotsus Manifold Addmiting a Semi-Symmetric Non -Metric Connection, Pure and Applied Mathematics Journal 4(1-2) (2015) 14-18.
• İ. Ünal, On Submanifolds of N(k)-Quasi Einstein Manifolds with Semi-Symmetric Metric Connection, Universal Journal of Mathematics and Applications 3(4) (2020) 167-172.
• M. A. Akyol, S. Beyendi, Riemannian Submersions Endowed with a Semi-Symmetric Non-Metric Connection, Konuralp Journal of Mathematics, 6(1) (2018) 188-193.
• P. Baird, J. C. Wood., Harmonic Morphisms between Riemannian Manifolds, London Mathematical Society Monographs, 29, Oxford University Press, the Clarendon Press. Oxford, 2003.