Skip to main content
Log in

Abstract

We introduce the notion of Golden Riemannian manifolds of type (rs) and starting from a Golden Riemannian structure, we construct some remarkable classes of the induced structures on Riemannian manifold. Concret examples are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Blair, D.E.: Riemannian geometry of contact and symplectic manifolds. Progress in mathematics, vol. 203. Birhauser, Boston (2002)

    Book  Google Scholar 

  • Boothby, W.M.: Homogeneous complex contact manifolds. Proc. Symp. AMS III Differ. Geom. pp. 144–154 (1961)

  • Calabi, E.: Métriques kählériennes et fibrés holomorphes. Ann. Sci. Econ. Norm. Sup. 12, 269–294 (1979)

    Article  Google Scholar 

  • Crasmareanu, M., Hretecanu, C.E.: Golden differential geometry. Chaos Soliton. Fractal. 38, 1124–1146 (2008). https://doi.org/10.1016/j.chaos.2008.04.007

    Article  MathSciNet  Google Scholar 

  • Crasmareanu, M., Hretcanu, C.E.: Applications of the Golden ratio on Riemannian manifolds. Turkish J. Math. 33, 179191 (2009)

    MathSciNet  MATH  Google Scholar 

  • Etayo, F., Santamaria, R., Upadhyay, A.: On the geometry of almost Golden Riemannian manifolds. Mediterr. J. Math. 14, 187 (2017). https://doi.org/10.1007/s00009-017-0991-x

  • Gezer, A., Cengiz, N., Salimov, A.: On integrability of Golden Riemannian structures. Turkish J. Math. 37, 693–703 (2013)

    MathSciNet  MATH  Google Scholar 

  • Ishihara, S., Konish, Mi: Complex almost contact manifolds. Kodai Math. J. 3, 385–396 (1980)

    Article  MathSciNet  Google Scholar 

  • Ishihara, S., Konish, Mi,: Complex almost contact manifolds in Complex almost contact manifold. Kodai Math. J 5, 30–37 (1982)

    Article  MathSciNet  Google Scholar 

  • Kobayashi, S.: Remarks on complex contact manifolds. Proc. Am. Math. Soc. 10, 164–167 (1959)

    Article  MathSciNet  Google Scholar 

  • Kuo, Y.: On almost contact 3-structures. Tohoku Math. J. 2(22), 325–332 (1970)

    Article  Google Scholar 

  • Watson, B.: Riemannian submersions and instantons. Math. Modell. 1, 381–393 (1980)

    Article  MathSciNet  Google Scholar 

  • Watson, B.: G,G-Riemannian submersions and non-linear gauge fleld equations of general relativity. In: Rassias, T.M. (ed.) Global Analysis-Analysis in Manifolds, vol. 57, pp. 324–349. Teubner-Texte Math, Teubner, Leipzig (1983)

    Google Scholar 

  • Yano, K., Kon, M.: Structures on Manifolds. Series in Pure Mathematics, vol. 3. World Science, New York (1984)

    MATH  Google Scholar 

Download references

Acknowledgements

The author would like to thank the referee for his helpful suggestions and his valuable comments which helped to improve the manuscript.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Beldjilali Gherici.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gherici, B. Induced structures on Golden Riemannian manifolds. Beitr Algebra Geom 59, 761–777 (2018). https://doi.org/10.1007/s13366-018-0392-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13366-018-0392-8

Keywords

Mathematics Subject Classification

Navigation