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

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.

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

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.

___

  • 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.