SG-Lightlike Submanifolds of a Locally Bronze Semi-Riemannian Manifold Equipped With (l,m)-Type Connection
Abstract
This research work introduces the geometry of the SG (Screen Generic)-lightlike submanifolds of a locally bronze semi-Riemannian manifold endowed with an (l,m)-type connection. The characterization theorems on geodesicity of such submanifolds with respect to the integrability and parallelism of the distributions are established. It is shown that there exists no coisotropic, isotropic or totally proper SG-lightlike submanifold of a locally bronze semi-Riemannian manifold. Assertions for the smooth transversal vector fields in totally umbilical proper SG-lightlike submanifold are obtained. Furthermore, the structure of a minimal SG-lightlike submanifold of a locally bronze semi-Riemannian manifold is detailed with an example.
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References
V. W. De Spinadel, “On characterization of the onset to chaos,” Chaos, Solitons & Fractals, vol. 8, no. 10, pp. 1631–1643, 1997. https://doi.org/10.1016/S0960-0779(97)00001-5.
P. K. Pandey and S, “Bronze differential geometry,” Journal of Science and Arts, vol. 45, no. 4, pp. 973–980, 2018. https://www.josa.ro/index.html?https%3A//www.josa.ro/josa.html.
R. C. Akpinar, “On bronze Riemannian structures,” Advanced Studies: Euro-Tbilisi Mathematical Journal, vol. 13, no. 3, pp. 161–169, 2020. https://tcms.org.ge/Journals/ASETMJ/Volume13/Volume13_3/PDF/tmj13_3_13.pdf.
K. L. Duggal and A. Bejancu, Lightlike submanifolds of semi-Riemannian manifolds and applications. Kluwer Academic Publishers, Dordrecht, 1996. https://doi.org/10.1007/978-94-017-2089-2.
D. H. Jin and J. W. Lee, “Generic lightlike submanifolds of an indefinite cosymplectic manifold,” Mathematical Problems in Engineering, vol. 1, pp. 1–16, 2011. https://doi.org/10.1155/2011/610986.
K. L. Duggal and D. J. Jin, “Generic lightlike submanifolds of an indefinite Sasakian manifold,” International Electronic Journal of Geometry, vol. 5, no. 1, pp. 108–119, 2012.https://izlik.org/JA56MD26YU.
D. H. Jin, “Generic lightlike submanifolds of an indefinite Kaehler manifold with a semisymmetric non-metric connection,” Problemy Analiza -Issues of Analysis, vol. 7, no. 2, pp. 47–68, 2018. https://doi.org/10.15393/j3.art.2018.4650.
D. H. Jin, “Generic lightlike submanifolds of an indefinite Kaehler manifold with a non-metric ϕ-symmetric connection,” Communications of the Korean Mathematical Society, vol. 32, no. 4, pp. 1047–1065, 2017. https://doi.org/10.4134/CKMS.c170033.
B. Dogan, B. Sahin, and E. Yasar, “Screen generic lightlike submanifolds,” Mediterranean Journal of Mathematics, vol. 16, no. 4, pp. 1–21, 2019. https://doi.org/10.1007/S00009-019-1380-4.
R. S. Gupta, “Screen generic lightlike submanifolds of indefinite Sasakian manifolds,” Mediterranean Journal of Mathematics, vol. 17, no. 5, pp. 1–23, 2020. https://doi.org/10.1007/s00009-020-01590-8.
A. Yadav and S. Kumar, “Screen generic lightlike submanifolds of golden semi-Riemannian manifolds,” Mediterranean Journal of Mathematics, vol. 19, no. 6, pp. 1–19, 2022. https://doi.org/10.1007/s00009-022-02122-2.
N. Poyraz, “Screen generic lightlike submanifolds of indefinite cosymplectic manifolds,” Filomat, vol. 37, no. 24, pp. 8261–8277, 2023. https://doi.org/10.2298/FIL2324261P.
N. Poyraz, “Screen generic lightlike submanifolds of semi-Riemannian product manifolds,” Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 1, pp. 171–183, 2024. https://doi.org/10.15672/hujms.1168604.
D. H. Jin, “Lightlike hypersurfaces of an indefinite trans-Sasakian manifold with an (l, m)-type connection,” Journal of the Korean Mathematical Society, vol. 55, no. 5, pp. 1075–1089, 2018. https://doi.org/10.4134/JKMS.j170538.
D. H. Jin and C. W. Lee, “Generic lightlike submanifolds of an indefinite Kaehler manifold with an (l, m)-type connection,” Balkan Journal of Geometry and its Applications, vol. 25, no. 2, pp. 39–51, 2020. http://emis.maths.tcd.ie/journals/BJGA/v25n2/B25-2ji-ZBH18.pdf.
K. L. Duggal and D. H. Jin, “Totally umbilical lightlike submanifolds,” Kodai Mathematical Journal, vol. 26, no. 1, pp. 49–68, 2003. https://doi.org/10.2996/kmj/1050496648.
C. L. Bejan and K. L. Duggal, “Global lightlike manifolds and harmonicity,” Kodai Mathematical Journal, vol. 28, no. 1, pp. 131–145, 2005. https://doi.org/10.2996/kmj/1111588042
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