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The Mathematical Intelligencer

, Volume 40, Issue 2, pp 50–54 | Cite as

A Geometric Interpretation of Curvature Inequalities on Hypersurfaces via Ravi Substitutions in the Euclidean Plane

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References

  1. [1]
    Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado, Inequalities: A Mathematical Olympiad Approach, Birkhäuser, 2009.Google Scholar
  2. [2]
    Bang-Yen Chen, Mean Curvature and Shape Operator of Isometric Immersions in Real-Space-Forms, Glasgow Math. J., 38 (1996), pp. 87–97.Google Scholar
  3. [3]
    Bang-Yen Chen, Pseudo-Riemannian Geometry, \(\delta\) –Invariants and Applications, World Scientific, 2011.Google Scholar
  4. [4]
    Alfred Clebsch, Über die Anwendung der quadratischen Substitution auf die Gleichungen fÜnften Grades und die geometrische Theorie des ebenen FÜnfseits, Mathematische Annalen, 4 (1871), pp. 284–345.Google Scholar
  5. [5]
    Zdravko Cvetkovski, Inequalities, Theorems, Techniques and Selected Problems, Springer-Verlag, 2012.Google Scholar
  6. [6]
    M. P. do Carmo, Riemannian Geometry, Birkhäuser, 1992.Google Scholar
  7. [7]
    Leonhard Euler, Solutio facilis problematum quorundam geometricorum difficillimorum, Novi Commentarii academiae scien-tiarum Petropolitanae, 11 (1767), pp. 103–123.Google Scholar
  8. [8]
    C. F. Gauss, Disquisitiones circa superficies curvas, Typis Dieterichianis, Goettingen, 1828.Google Scholar
  9. [9]
    Sophie Germain, Mémoire sur la courbure des surfaces, Journal für die reine und andewandte Mathematik, Herausgegeben von A. L. Crelle, Siebenter Band, pp. 1–29, Berlin, 1831.Google Scholar
  10. [10]
    David Hilbert and S. Cohn-Vossen, Geometry and the Imagination, trans. by P. Nemenyi, New York: Chelsea Pub., 1952; recent edition: AMS Chelsea Publishing, American Mathematical Society, Providence, RI, 1999.Google Scholar
  11. [11]
    Felix Klein, Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade, Teubner, Leipzig, 1884.Google Scholar
  12. [12]
    François Lê, Alfred Clebsch’s “geometrical clothing” of the theory of the quintic equation, Arch. Hist. Exact Sci., 71 (2017), no. 1, 39–70.Google Scholar
  13. [13]
    Emil Stoica, Nicuşor Minculete and Cătălin Barbu, New Aspects of Ionescu–Weitzenbock’s Inequality, Balkan Journal of Geometry and Its Applications, 21 (2016), no. 2, pp. 95–101.Google Scholar
  14. [14]
    B. D. Suceavă, The Amalgamatic Curvature and the Orthocurvatures of Three-Dimensional Hypersurfaces in \({\mathbb{E}}^4\), Publicationes Mathematicae, 87 (2015), nos. 1–2, pp. 35–46.Google Scholar

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© Springer Science+Business Media, LLC 2018

Authors and Affiliations

  1. 1.California State University FullertonFullertonUSA

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