대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제39권2호
  • /
  • Pages.493-511
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  • 2024
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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INVARIANT NULL RIGGED HYPERSURFACES OF INDEFINITE NEARLY α-SASAKIAN MANIFOLDS

  • Mohamed H. A. Hamed (School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal) ;
  • Fortune Massamba (School of Mathematics, Statistics and Computer Science University of KwaZulu-Natal)
  • 투고 : 2023.09.07
  • 심사 : 2024.01.25
  • 발행 : 2024.04.30
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초록

We introduce invariant rigged null hypersurfaces of indefinite almost contact manifolds, by paying attention to those of indefinite nearly α-Sasakian manifolds. We prove that, under some conditions, there exist leaves of the integrable screen distribution of the ambient manifolds admitting nearly α-Sasakian structures.

키워드

과제정보

Mohamed H. A. Hamed would like to thank the Simons Foundation through the RGSM-Project for financial support. The authors thank the referee for helping them to improve the presentation.

참고문헌

  1. D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, 203, Birkhauser Boston, Inc., Boston, MA, 2002. https://doi.org/10.1007/978-1-4757-3604-5
  2. K. L. Duggal and A. Bejancu, Lightlike submanifolds of semi-Riemannian manifolds and applications, Mathematics and its Applications, 364, Kluwer Acad. Publ., Dordrecht, 1996. https://doi.org/10.1007/978-94-017-2089-2
  3. K. L. Duggal and B. Sahin, Differential geometry of lightlike submanifolds, Frontiers in Mathematics, Birkhauser Verlag, Basel, 2010. https://doi.org/10.1007/978-3-0346-0251-8
  4. M. Gutierrez and B. Olea, Induced Riemannian structures on null hypersurfaces, Math. Nachr. 289 (2016), no. 10, 1219-1236. https://doi.org/10.1002/mana.201400355
  5. D. N. Kupeli, Singular semi-Riemannian geometry, Mathematics and its Applications, 366, Kluwer Acad. Publ., Dordrecht, 1996. https://doi.org/10.1007/978-94-015-8761-7
  6. F. Massamba, Totally contact umbilical lightlike hypersurfaces of indefinite Sasakian manifolds, Kodai Math. J. 31 (2008), no. 3, 338-358. https://doi.org/10.2996/kmj/1225980441
  7. F. Massamba, On semi-parallel lightlike hypersurfaces of indefinite Kenmotsu manifolds, J. Geom. 95 (2009), no. 1-2, 73-89. https://doi.org/10.1007/s00022-010-0021-7
  8. F. Massamba, On lightlike geometry in indefinite Kenmotsu manifolds, Math. Slovaca 62 (2012), no. 2, 315-344. https://doi.org/10.2478/s12175-012-0012-2
  9. F. Massamba, Screen almost conformal lightlike geometry in indefinite Kenmotsu space forms, Int. Electron. J. Geom. 5 (2012), no. 2, 36-58.
  10. F. Massamba, Symmetries of null geometry in indefinite Kenmotsu manifolds, Mediterr. J. Math. 10 (2013), no. 2, 1079-1099. https://doi.org/10.1007/s00009-012-0205-5
  11. F. Massamba, Screen conformal invariant lightlike hypersurfaces of indefinite Sasakian space forms, Afr. Diaspora J. Math. 14 (2013), no. 2, 22-37.
  12. F. Massamba, Almost Weyl structures on null geometry in indefinite Kenmotsu manifolds, Math. Slovaca 66 (2016), no. 6, 1443-1458. https://doi.org/10.1515/ms-2016-0235
  13. F. Massamba and S. Ssekajja, Quasi generalized CR-lightlike submanifolds of indefinite nearly Sasakian manifolds, Arab. J. Math. (Springer) 5 (2016), no. 2, 87-101. https://doi.org/10.1007/s40065-016-0146-0
  14. F. Massamba and S. Ssekajja, A note on quasi-generalized CR-lightlike geometry in indefinite nearly μ-Sasakian manifolds, Int. J. Geom. Methods Mod. Phys. 14 (2017), no. 3, 1750045, 17 pp. https://doi.org/10.1142/S0219887817500451
  15. F. Ngakeu and H. F. Tetsing, α-associated metrics on rigged null hypersurfaces, Turkish J. Math. 43 (2019), no. 3, 1161-1181. https://doi.org/10.3906/mat-1810-107
  16. B. O'Neill, Semi-Riemannian geometry, Pure and Applied Mathematics, 103, Academic Press, Inc., New York, 1983.
  17. H. F. Tetsing, F. Ngakeu, and B. Olea, Rigging technique for 1-lightlike submanifolds and preferred rigged connections, Mediterr. J. Math. 16 (2019), no. 6, Paper No. 139, 20 pp. https://doi.org/10.1007/s00009-019-1423-x
  18. K. Yano and M. Kon, Structures on manifolds, Series in Pure Mathematics, 3, World Sci. Publishing, Singapore, 1984.