Bi-slant lightlike submanifolds of golden semi-Riemannian manifolds

Muqeem Ahmad; Mobin Ahmad; Fatemah Mofarreh; Muqeem Ahmad; Mobin Ahmad; Fatemah Mofarreh

doi:10.3934/math.2023996

AIMS Mathematics

2023, Volume 8, Issue 8: 19526-19545. doi: 10.3934/math.2023996

Previous Article Next Article

Research article

Bi-slant lightlike submanifolds of golden semi-Riemannian manifolds

1.
Department of Mathematics & Statistics, Integral University, Kursi Road, Lucknow, 226026, India
2.
Department of Mathematical Science, Faculty of Science, Princess Nourah bint Abdulrahman University, P.O. Box 13415, Saudi Arabia

Received: 16 March 2023 Revised: 18 May 2023 Accepted: 04 June 2023 Published: 09 June 2023
MSC : 53C15, 53C25, 53C40, 53C50

In this paper, we introduce the notion of a bi-slant lightlike submanifold of a golden semi-Riemannian manifold. We provide two examples. We give some characterizations about the geometry of such submanifolds.
- degenerate metric,
- indefinite metrics,
- bi-slant lightlike submanifold,
- golden structure,
- golden semi-Riemannian manifold
Citation: Muqeem Ahmad, Mobin Ahmad, Fatemah Mofarreh. Bi-slant lightlike submanifolds of golden semi-Riemannian manifolds[J]. AIMS Mathematics, 2023, 8(8): 19526-19545. doi: 10.3934/math.2023996

Related Papers:

Abstract

In this paper, we introduce the notion of a bi-slant lightlike submanifold of a golden semi-Riemannian manifold. We provide two examples. We give some characterizations about the geometry of such submanifolds.

References

[1]	K. L. Duggal, A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Dordrecht: Springer, 1996. https://doi.org/10.1007/978-94-017-2089-2
[2]	K. L. Duggal, B. Sahin, Differential Geomety of Lightlike Submanifolds, Basel: Birkhauser Verlag, 2010. https://doi.org/10.1007/978-3-0346-0251-8
[3]	N. Poyraz, E. Yasar, Lightlike submanifolds of golden semi-Riemannian manifolds, J. Geom. Phys., 141 (2019), 92–104. https://doi.org/10.1016/j.geomphys.2019.03.008 doi: 10.1016/j.geomphys.2019.03.008
[4]	B. Y. Chen, Geometry of slant submanifolds, KU Leuven, 1990. https://doi.org/10.48550/arXiv.1307.1512
[5]	A. Lotta, Slant submanifolds in contact geometry, Bull. Math. Soc. Sci. Math., 39 (1996), 183–198.
[6]	B. Sahin, Slant submanifolds of an almost product Riemannian manifold, J. Korean Math. Soc., 43 (2006), 717–732. https://doi.org/10.4134/JKMS.2006.43.4.717 doi: 10.4134/JKMS.2006.43.4.717
[7]	J. L. Cabrerizo, A. Carriazo, L. M. Fernandez, M. Fernandez, Slant submanifolds in Sasakian manifolds, Glasgow Math. J., 42 (2000), 125–138. https://doi.org/10.1017/S0017089500010156 doi: 10.1017/S0017089500010156
[8]	M. A. Khan, K. Singh, V. A. Khan, Slant submanifolds of LP-contact manifolds, Differ. Geom., 12 (2010), 102–108.
[9]	N. Papaghiuc, Semi-slant submanifolds of a Kaehlerian manifold, An. Stiint. Univ. Al. I. Cuza Iasi. Mat., 40 (1994), 5561.
[10]	P. Alegre, A. Carriazo, Bi-slant submanifolds of para Hermitian manifolds, Mathematics, 7 (2019), 618. https://doi.org/10.3390/math7070618 doi: 10.3390/math7070618
[11]	M. Crasmareanu, C. E. Hretcanu, Golden differential geometry, Chaos Solitons Fractals, 38 (2008), 1229–1238. https://doi.org/10.1016/j.chaos.2008.04.007
[12]	C. E. Hretcanu, M. Crasmareanu, Applications of the golden ratio on Riemannian manifolds, Turk. J. Math., 33 (2009), 179–191. https://doi.org/10.3906/mat-0711-29 doi: 10.3906/mat-0711-29
[13]	M. A. Qayyoom, M. Ahmad, Hypersurfaces immersed in a golden Riemannian manifold, Afr. Mat., 33 (2022), 3. https://doi.org/10.1007/s13370-021-00954-x doi: 10.1007/s13370-021-00954-x
[14]	M. Ahmad, M. A. Qayyoom, Warped product skew semi-invariant submanifolds of locally golden Riemannian manifold, Honam Math. J., 44 (2022), 1–16. https://doi.org/10.5831/HMJ.2022.44.1.1 doi: 10.5831/HMJ.2022.44.1.1
[15]	M. Ahmad, M. A. Qayyoom, Skew semi-invariant submanifolds of a golden Riemannian manifold, J. Math. Control Sci. Appl., 7 (2021), 45–56.
[16]	M. Ahmad, M. A. Qayyoom, Geometry of submanifolds of locally metallic Riemannian manifolds, Ganita, 71 (2021), 125–144.
[17]	B. Sahin, Slant lightlike submanifolds of indefinite Hermitian manifolds, Balkan J. Geom. Appl., 13 (2008), 107–119.
[18]	R. S. Gupta, A. Sharfuddin, Slant lightlike submanifolds of indefinite Kenmotsu manifolds, Turk. J. Math., 35 (2011), 115–127. https://doi.org/10.3906/mat-0906-52 doi: 10.3906/mat-0906-52
[19]	J. W. Lee, D. H. Jin, Slant lightlike submanifolds of an indefinite Sasakian manifold, J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math., 19 (2012), 111–125. https://doi.org/10.7468/jksmeb.2012.19.2.111 doi: 10.7468/jksmeb.2012.19.2.111
[20]	V. Khan, M. Khan, K. Khan, Slant and semi-slant submanifolds of a Kenmotsu manifold, Math. Slovaca, 57 (2007), 483–494. https://doi.org/10.2478/s12175-007-0040-5 doi: 10.2478/s12175-007-0040-5
[21]	S. S. Shukla, A. Yadav, Semi-slant lightlike submanifolds of indefinite Sasakian manifolds, Kyungpook Math. J., 56 (2016), 625–638. https://doi.org/10.5666/kmj.2016.56.2.625 doi: 10.5666/kmj.2016.56.2.625
[22]	S. S. Shukla, A. Yadav, Semi-slant lightlike submanifolds of indefinite Kaehler manifolds, Rev. Unión Mat. Argent., 56 (2015), 21–27.
[23]	H. Li, X. Liu, Semi-slant submanifolds of a locally product manifold, Georgian Math. J., 12 (2005), 273–282. https://doi.org/10.1515/gmj.2005.273 doi: 10.1515/gmj.2005.273
[24]	R. Prasad, A. Haseeb, S. Singh, Quasi bi-slant submanifolds of para-Kenmotsu manifolds, Balk. J. Geom. its Appl., 26 (2021), 100–111.
[25]	S. S. Shukla, P. Kumar, Quasi-bi-slant lightlike submanifolds of indefinite Kaehler manifolds, J. Math. Comput. Sci., 11 (2021), 2439–2465. https://doi.org/10.28919/jmcs/5562 doi: 10.28919/jmcs/5562
[26]	S. Kumar, A. Yadv, Semi-slant lightlike submanifolds of golden semi-Riemannian manifolds, Kragujev. J. Math., 49 (2022), 141–158.
[27]	D. L. Johnson, L. B. Whitt, Totally geodesic foliations, J. Differ. Geom., 15 (1980), 225235.
[28]	B. Sahin, Screen transversal lightlike submanifolds of indefinite Kaehler manifolds, Chaos Solitons Fractals, 38 (2008), 1439–1448. https://doi.org/10.1016/j.chaos.2008.04.008 doi: 10.1016/j.chaos.2008.04.008

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)