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Golden differential geometry

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  • Crasmareanu, Mircea
  • Hreţcanu, Cristina-Elena

Abstract

A research on the properties of the Golden structure (i.e. a polynomial structure with the structure polynomial Q(X)=X2-X-I) is carried out in this article. The Golden proportion plays a central role in this paper. The geometry of the Golden structure on a manifold is investigated by using a corresponding almost product structure.

Suggested Citation

  • Crasmareanu, Mircea & Hreţcanu, Cristina-Elena, 2008. "Golden differential geometry," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1229-1238.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:5:p:1229-1238
    DOI: 10.1016/j.chaos.2008.04.007
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    References listed on IDEAS

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    1. Marek-Crnjac, L., 2006. "The golden mean in the topology of four-manifolds, in conformal field theory, in the mathematical probability theory and in Cantorian space-time," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1113-1118.
    2. Marek Crnjac, L., 2005. "Periodic continued fraction representations of different quark’s mass ratios," Chaos, Solitons & Fractals, Elsevier, vol. 25(4), pages 807-814.
    3. Stakhov, A. & Rozin, B., 2006. "The “golden” algebraic equations," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1415-1421.
    4. Sigalotti, Leonardo Di G. & Mejias, Antonio, 2006. "The golden ratio in special relativity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 521-524.
    5. Stakhov, Alexey, 2006. "Fundamentals of a new kind of mathematics based on the Golden Section," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1124-1146.
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    Cited by:

    1. El Naschie, M.S., 2008. "Eliminating gauge anomalies via a “point-less” fractal Yang–Mills theory," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1332-1335.
    2. Marek-Crnjac, L. & Iovane, G. & Nada, S.I. & Zhong, Ting, 2009. "The mathematical theory of finite and infinite dimensional topological spaces and its relevance to quantum gravity," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 1974-1979.
    3. Elokaby, A., 2009. "Confinement and asymptotic freedom seen with a golden eye," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2592-2594.
    4. Khan, Mohammad Nazrul Islam, 2021. "Novel theorems for the frame bundle endowed with metallic structures on an almost contact metric manifold," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. Cristina E. Hretcanu & Adara M. Blaga, 2021. "Warped Product Submanifolds in Locally Golden Riemannian Manifolds with a Slant Factor," Mathematics, MDPI, vol. 9(17), pages 1-15, September.
    6. Cristina E. Hretcanu & Adara M. Blaga, 2021. "Types of Submanifolds in Metallic Riemannian Manifolds: A Short Survey," Mathematics, MDPI, vol. 9(19), pages 1-22, October.
    7. El Naschie, M.S., 2008. "An energy balance Eigenvalue equation for determining super strings dimensional hierarchy and coupling constants," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1283-1285.
    8. El Naschie, M.S., 2009. "The theory of Cantorian spacetime and high energy particle physics (an informal review)," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2635-2646.
    9. El Naschie, M.S., 2009. "On the Witten–Duff five Branes model together with knots theory and E8E8 super strings in a single fractal spacetime theory," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2018-2021.
    10. Majid Ali Choudhary & Khaled Mohamed Khedher & Oğuzhan Bahadır & Mohd Danish Siddiqi, 2021. "On Golden Lorentzian Manifolds Equipped with Generalized Symmetric Metric Connection," Mathematics, MDPI, vol. 9(19), pages 1-18, September.

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