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Screen Semi-invariant Lightlike Submanifolds of a Golden Semi-Riemannian Manifold

Year 2022, Volume: 3 Issue: 1, 1 - 11, 30.06.2022

Abstract

In this paper, we study the geometry of screen semi-invariant lightlike submanifolds of a golden semi-Riemannian manifold. The intergrability conditions of distributions S(TN) and RadTN on screen semi-invariant lightlike submanifolds of a golden semi-Riemannian manifold are obtained. Further, we derive necessary and su_cient conditions for above distributions to be totally geodesic foliations.

References

  • Acet, B. E.; Erdogan, F. E.,; Perktas, S. Y., Lightlike submanifolds of a metallic semi- Riemannian manifold, arXiv Preprint, arXiv:1811.05019.
  • Crasmareanu, M.; Hretcanu, C. E., On some invariant submanifolds in a Riemannian manifold with golden structure, An. Stiins. Univ. Al. I. Cuza Iasi. Mat., 53 (2007), 199-211.
  • Crasmareanu, M.; Hretcanu, C. E., Golden di_erential geometry, Chaos, Solitons and Fractals, 38 (2008), 1229-1238.
  • Crasmareanu, M.; Hretcanu, C. E., Applications of the Golden ratio on Riemannian manifolds, Turk. J. Math., 33 (2009), 179-191.
  • Crnjac, L. M., On the mass spectrum of the elementary particles of the standard model using El Naschie's Golden _eld theory, Chaos, Solitons and Fractals, 15 (2003), 611-618.
  • Crnjac, L. M., The Golden mean in the topology of four-manifolds in conformal _eld theory, in the mathematical probability theory and in Cantorian spacetime, Chaos, Solitons and Fractals, 28 (2006), 1113-1118.
  • De Spinadel, V. W., The metallic means family and renormalization group techniques, Control in Dynamic Systems, 6 (2000), 173-189.
  • Duggal, K. L.; Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publisher, 1996.
  • Duggal, K. L.; Sahin, B., Di_erential Geometry of Lightlike Submanifolds, Birkhauser Verlag AG, Berlin, 2010.
  • Duggal, K. L.; Sahin B., Lightlike submanifolds of inde_nite Sasakian manifolds, In- ternational Journal of Mathematics and Mathematical Sciences, 2007 (2007), 1-21.
  • Erdogan, F. E.; Yildirim C., Semi-invariant submanifolds of Golden Riemannian mani- folds, AIP Conference proceeding, 1833, (2017).
  • Gezer, A.; Cengiz, N.; Salimov, A., On integrability of Golden Riemannian structures, Turk. J. Math., 37 (2013), 693-703.
  • Livio, M., The Golden Ratio: The Story of phi, the World's Most Astonishing Number, Broadway, 2002.

Screen Semi-invariant Lightlike Submanifolds of a Golden Semi-Riemannian Manifold

Year 2022, Volume: 3 Issue: 1, 1 - 11, 30.06.2022

Abstract

In this paper, we study the geometry of screen semi-invariant lightlike submanifolds of a golden semi-Riemannian manifold. The intergrability conditions of distributions S(TN) and RadTN on screen semi-invariant lightlike submanifolds of a golden semi-Riemannian manifold are obtained. Further, we derive necessary and su_cient conditions for above distributions to be totally geodesic foliations.

References

  • Acet, B. E.; Erdogan, F. E.,; Perktas, S. Y., Lightlike submanifolds of a metallic semi- Riemannian manifold, arXiv Preprint, arXiv:1811.05019.
  • Crasmareanu, M.; Hretcanu, C. E., On some invariant submanifolds in a Riemannian manifold with golden structure, An. Stiins. Univ. Al. I. Cuza Iasi. Mat., 53 (2007), 199-211.
  • Crasmareanu, M.; Hretcanu, C. E., Golden di_erential geometry, Chaos, Solitons and Fractals, 38 (2008), 1229-1238.
  • Crasmareanu, M.; Hretcanu, C. E., Applications of the Golden ratio on Riemannian manifolds, Turk. J. Math., 33 (2009), 179-191.
  • Crnjac, L. M., On the mass spectrum of the elementary particles of the standard model using El Naschie's Golden _eld theory, Chaos, Solitons and Fractals, 15 (2003), 611-618.
  • Crnjac, L. M., The Golden mean in the topology of four-manifolds in conformal _eld theory, in the mathematical probability theory and in Cantorian spacetime, Chaos, Solitons and Fractals, 28 (2006), 1113-1118.
  • De Spinadel, V. W., The metallic means family and renormalization group techniques, Control in Dynamic Systems, 6 (2000), 173-189.
  • Duggal, K. L.; Bejancu, A., Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Kluwer Academic Publisher, 1996.
  • Duggal, K. L.; Sahin, B., Di_erential Geometry of Lightlike Submanifolds, Birkhauser Verlag AG, Berlin, 2010.
  • Duggal, K. L.; Sahin B., Lightlike submanifolds of inde_nite Sasakian manifolds, In- ternational Journal of Mathematics and Mathematical Sciences, 2007 (2007), 1-21.
  • Erdogan, F. E.; Yildirim C., Semi-invariant submanifolds of Golden Riemannian mani- folds, AIP Conference proceeding, 1833, (2017).
  • Gezer, A.; Cengiz, N.; Salimov, A., On integrability of Golden Riemannian structures, Turk. J. Math., 37 (2013), 693-703.
  • Livio, M., The Golden Ratio: The Story of phi, the World's Most Astonishing Number, Broadway, 2002.
There are 13 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Gauree Shanker This is me 0000-0003-1477-6427

Ramandeep Kaur 0000-0002-2526-2459

Ankit Yadav This is me 0000-0002-3366-2524

Early Pub Date June 25, 2022
Publication Date June 30, 2022
Submission Date December 18, 2021
Published in Issue Year 2022 Volume: 3 Issue: 1

Cite

Vancouver Shanker G, Kaur R, Yadav A. Screen Semi-invariant Lightlike Submanifolds of a Golden Semi-Riemannian Manifold. BUTS. 2022;3(1):1-11.
This journal is prepared and published by the Bingöl University Technical Sciences journal team.