Research Article
BibTex RIS Cite
Year 2019, Volume: 11 Issue: 1, 8 - 23, 30.06.2019

Abstract

References

  • Ahmad M., Jun, J. B., Haseeb A., Submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric semi-metric connection, Tensor, N. S., 70(2008), 311--321.
  • Ahmad M., Jun, J. B., Haseeb A., Submanifolds of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric non-metric connection, J. Chungcheong Math. Soc., 24(1)(2011), 91--104.
  • Ahmad M., Al-Hossain A.Y., Ojha, J.P., On submanifolds of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric metric connection, Theoretical Mathematics and Application, 4(4)(2014), 1--17.
  • Bahadir, O., Uddin, S., Slant submanifolds of golden Riemannian manifolds, arXiv:1804.11126v1.
  • Blaga, A.M., Hretcanu, C. E., Invariant, anti-invariant and slant submanifolds of a metallic Riemannian manifold, arXiv: 1803.01415.
  • Crasmareanu, M., Hretcanu, C.E., Golden differential geometry, Chaos Solitons Fractals, 38(5)(2008), 1229--1238.
  • Crasmareanu, M., Hretcanu, C.E., On some invariant submanifolds in a Riemannian manifold with golden structure, Analele Stintifice Universitatis "Al. I. Cuza" DIN IASI (S.N.) Matematica, Tomul LIII (2007), 199--211.
  • Das L. S., Nivas R., Ali S., Ahmad M., Study of submanifolds in a manifold with quarter symmetric semi-metric connection, Tensor N. S., 65(2004), 250--260.
  • Etayo, F., Santamaria, R., Upadhyay, A., On the geometry of almost golden Riemannian manifolds, Mediterr. J. Math. 187(14)(2017), 991--1007.
  • Gezer, A., Cengiz, N., Salimov, A., On integrability of golden Riemannian structures, Turk.J.Math., 37(2013), 366--703.
  • Gherici, B., Induced structure on golden Riemannian manifolds, Beitr Algebra Geom., 18(8)(2018), 366--392.
  • Goldberg, S.I., Yano, K., Polynomial structures on manifolds, Kodai Maths.Sem. Rep., 22(2)(1970), 199--218.
  • Hretcanu, C.E., Submanifolds in Riemannian manifold with golden structure, Workshop on Finsler geometry and its applications, Hungary (2007).
  • Hretcanu, C.E., Induced structure on submanifolds in almost product Riemannian manifolds, arXiv:math/0608533.
  • Hretcanu, C.E., Crasmareanu, M., Metallic structure on Riemannian manifolds, Revista De La Union Mathematica Argentina, 54(2)(2013), 15--27.
  • Hretcanu, C.E., Blaga, A.M., Submanifolds in metallic Riemannian manifolds, arXiv:1803.02184.
  • Ozkan, M., Prolongations of golden structures to tangent bundles, Differential Geometry - Dynamical Systems, 16(2014), 227--238.
  • Ozgur, C., Ahmad, M., Haseeb, A., CR-submanifolds of LP-Sasakian manifolds with semi-symmetric metric connection, Hacettepe J. Math. And Stat., 39(4)(2010), 489--496.
  • Poyraz, N.O., Erol, Y., Lightlike hypersurfaces of a golden semi-Riemannian manifold, Mediterr. J. Math., (2017) 14:204, DOI 10.1007/s00009-017-0999-2.

On Submanifolds in a Riemannian Manifold with Golden Structure

Year 2019, Volume: 11 Issue: 1, 8 - 23, 30.06.2019

Abstract

A golden Riemannian structure $(J,g)$ on a Riemannian  manifold is given by a tensor field $J$ of type $(1,1)$ satisfying the golden section relation $J^{2}=J+I,$ and a pure Riemannian metric $g$, that is  a metric satisfying $g(JX,Y)=g(X,JY).$ We investigate  some fundamental properties of the induced structure on submanifolds immersed in golden Riemannian manifolds. We obtain effective relations for some induced structures on submanifolds of codimension 2. We also construct an example on submanifold of a golden Riemannian manifold.

References

  • Ahmad M., Jun, J. B., Haseeb A., Submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric semi-metric connection, Tensor, N. S., 70(2008), 311--321.
  • Ahmad M., Jun, J. B., Haseeb A., Submanifolds of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric non-metric connection, J. Chungcheong Math. Soc., 24(1)(2011), 91--104.
  • Ahmad M., Al-Hossain A.Y., Ojha, J.P., On submanifolds of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric metric connection, Theoretical Mathematics and Application, 4(4)(2014), 1--17.
  • Bahadir, O., Uddin, S., Slant submanifolds of golden Riemannian manifolds, arXiv:1804.11126v1.
  • Blaga, A.M., Hretcanu, C. E., Invariant, anti-invariant and slant submanifolds of a metallic Riemannian manifold, arXiv: 1803.01415.
  • Crasmareanu, M., Hretcanu, C.E., Golden differential geometry, Chaos Solitons Fractals, 38(5)(2008), 1229--1238.
  • Crasmareanu, M., Hretcanu, C.E., On some invariant submanifolds in a Riemannian manifold with golden structure, Analele Stintifice Universitatis "Al. I. Cuza" DIN IASI (S.N.) Matematica, Tomul LIII (2007), 199--211.
  • Das L. S., Nivas R., Ali S., Ahmad M., Study of submanifolds in a manifold with quarter symmetric semi-metric connection, Tensor N. S., 65(2004), 250--260.
  • Etayo, F., Santamaria, R., Upadhyay, A., On the geometry of almost golden Riemannian manifolds, Mediterr. J. Math. 187(14)(2017), 991--1007.
  • Gezer, A., Cengiz, N., Salimov, A., On integrability of golden Riemannian structures, Turk.J.Math., 37(2013), 366--703.
  • Gherici, B., Induced structure on golden Riemannian manifolds, Beitr Algebra Geom., 18(8)(2018), 366--392.
  • Goldberg, S.I., Yano, K., Polynomial structures on manifolds, Kodai Maths.Sem. Rep., 22(2)(1970), 199--218.
  • Hretcanu, C.E., Submanifolds in Riemannian manifold with golden structure, Workshop on Finsler geometry and its applications, Hungary (2007).
  • Hretcanu, C.E., Induced structure on submanifolds in almost product Riemannian manifolds, arXiv:math/0608533.
  • Hretcanu, C.E., Crasmareanu, M., Metallic structure on Riemannian manifolds, Revista De La Union Mathematica Argentina, 54(2)(2013), 15--27.
  • Hretcanu, C.E., Blaga, A.M., Submanifolds in metallic Riemannian manifolds, arXiv:1803.02184.
  • Ozkan, M., Prolongations of golden structures to tangent bundles, Differential Geometry - Dynamical Systems, 16(2014), 227--238.
  • Ozgur, C., Ahmad, M., Haseeb, A., CR-submanifolds of LP-Sasakian manifolds with semi-symmetric metric connection, Hacettepe J. Math. And Stat., 39(4)(2010), 489--496.
  • Poyraz, N.O., Erol, Y., Lightlike hypersurfaces of a golden semi-Riemannian manifold, Mediterr. J. Math., (2017) 14:204, DOI 10.1007/s00009-017-0999-2.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mobin Ahmad

Mohammad Aamir Qayyoom 0000-0001-5942-1561

Publication Date June 30, 2019
Published in Issue Year 2019 Volume: 11 Issue: 1

Cite

APA Ahmad, M., & Qayyoom, M. A. (2019). On Submanifolds in a Riemannian Manifold with Golden Structure. Turkish Journal of Mathematics and Computer Science, 11(1), 8-23.
AMA Ahmad M, Qayyoom MA. On Submanifolds in a Riemannian Manifold with Golden Structure. TJMCS. June 2019;11(1):8-23.
Chicago Ahmad, Mobin, and Mohammad Aamir Qayyoom. “On Submanifolds in a Riemannian Manifold With Golden Structure”. Turkish Journal of Mathematics and Computer Science 11, no. 1 (June 2019): 8-23.
EndNote Ahmad M, Qayyoom MA (June 1, 2019) On Submanifolds in a Riemannian Manifold with Golden Structure. Turkish Journal of Mathematics and Computer Science 11 1 8–23.
IEEE M. Ahmad and M. A. Qayyoom, “On Submanifolds in a Riemannian Manifold with Golden Structure”, TJMCS, vol. 11, no. 1, pp. 8–23, 2019.
ISNAD Ahmad, Mobin - Qayyoom, Mohammad Aamir. “On Submanifolds in a Riemannian Manifold With Golden Structure”. Turkish Journal of Mathematics and Computer Science 11/1 (June 2019), 8-23.
JAMA Ahmad M, Qayyoom MA. On Submanifolds in a Riemannian Manifold with Golden Structure. TJMCS. 2019;11:8–23.
MLA Ahmad, Mobin and Mohammad Aamir Qayyoom. “On Submanifolds in a Riemannian Manifold With Golden Structure”. Turkish Journal of Mathematics and Computer Science, vol. 11, no. 1, 2019, pp. 8-23.
Vancouver Ahmad M, Qayyoom MA. On Submanifolds in a Riemannian Manifold with Golden Structure. TJMCS. 2019;11(1):8-23.