Transversal Lightlike Submersions

Year 2024, Volume: 10 Issue: 2, 476 - 492, 25.06.2024

Esra Karataş , Cumali Yıldırım

https://doi.org/10.28979/jarnas.1440658

Abstract

In this paper, we introduce the concept of transversal lightlike submersions from semi-Riemannian manifolds onto semi-Riemannian manifolds. Specifically, we present the concepts of transversal r-lightlike and isotropic transversal lightlike submersions and examine the geometry of foliations formed by these submersions through various examples. In this way, we demonstrate certain points where transversal r-lightlike submersions differ from semi-Riemannian submersions. Furthermore, we investigate O’Neill’s tensors for transversal r-lightlike submersions and examine the integrability of certain distributions by employing these tensor fields. Thus, valuable information regarding such submersions’ geometric structures and properties can be provided, paving the way for new research avenues. We finally discuss the need for further research.

Keywords

Transversal submersion, Riemannian submersion, lightlike manifold, lightlike submersion

References

• B. O’Neill, The fundamental equations of a submersion, Michigan Mathematical Journal 13 (4) (1966) 459–469.
• A. Gray, Pseudo-Riemannian almost product manifolds and submersions, Journal of Mathematics and Mechanics 16 (7) (1967) 715–737.
• R. H. Escobales Jr, Riemannian submersions with totally geodesic fibers, Journal of Differential Geometry 10 (2) (1975) 253–276.
• S. Ianuş, R. Mazzocco, G. E. Vilcu, Riemannian submersions from quaternionic manifolds, Acta Applicandae Mathematicae 104 (2008) 83–89.
• V. N. Beretovskii, L. Guijarro, A metric characterization of Riemannian submersions, Annals of Global Analysis and Geometry 18 (6) (2000) 577–588.
• Ş. Eken Meriç, M. Gülbahar, E. Kılıç, Some inequalities for Riemannian submersions, Analele Stiintifice Ale Universitatii Al I Cuza Din Iasi-Serie Noua-Matematica 63 (3) (2017) 1–12.
• B. Şahin, Riemannian submersions from almost Hermitian manifolds, Taiwanese Journal of Mathematics 17 (2) (2013) 629–659.
• F. Narita, Riemannian submersion with isometric reflections with respect to the fibers, Kodai Mathematical Journal 16 (3) (1993) 416–427.
• M. A. Akyol, S. Beyendi, Riemannian submersions endowed with a semi-symmetric non-metric connection, Konuralp Journal of Mathematics 6 (1) (2018) 188–193.
• H. Demir, R. Sarı, Riemannian submersions with quarter-symmetric non-metric connection, Journal of Engineering Technology and Applied Sciences 6 (1) (2021) 1–8.
• E. Karataş, S. Zeren, M. Altin, Riemannian submersions endowed with a new type of semisymmetric non-metric connection, Thermal Science 27 (4B) (2023) 3393–3403.
• Y. Gündüzalp, On the geometry of Riemannian submersions, Master’s Thesis İnönü University (2007) Malatya.
• B. Şahin, Y. Gündüzalp, Submersion from semi-Riemannian manifolds onto lightlike manifolds, Hacettepe Journal of Mathematics and Statistics 39 (1) (2010), 41–53.
• B. Şahin, On a submersion between Reinhart lightlike manifolds and semi-Riemannian manifolds, Mediterranean Journal of Mathematics 5 (3) (2008) 273–284.
• K. L. Duggal, A. Bejancu, Lightlike submanifolds of semi-Riemannian manifolds and applications, Kluwer Academic, Dordrecht, 1996.
• K. Nomizu, Fundamentals of linear algebra, McGraw-Hill, New York, 1966.
• B. Sahin, Riemannian submersions, Riemannian maps in Hermitian geometry, and their applications, Academic Press, 2017.
• M. Falcitelli, S. Ianus, A. M. Pastore, Riemannian submersions and related topics, World Scientific, 2004.