Skip to main content

Advertisement

Log in

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

  • Article
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

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.

References

  1. Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado, Inequalities: A Mathematical Olympiad Approach, Birkhäuser, 2009.

  2. Bang-Yen Chen, Mean Curvature and Shape Operator of Isometric Immersions in Real-Space-Forms, Glasgow Math. J., 38 (1996), pp. 87–97.

  3. Bang-Yen Chen, Pseudo-Riemannian Geometry, \(\delta\) –Invariants and Applications, World Scientific, 2011.

  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.

  5. Zdravko Cvetkovski, Inequalities, Theorems, Techniques and Selected Problems, Springer-Verlag, 2012.

  6. M. P. do Carmo, Riemannian Geometry, Birkhäuser, 1992.

  7. Leonhard Euler, Solutio facilis problematum quorundam geometricorum difficillimorum, Novi Commentarii academiae scien-tiarum Petropolitanae, 11 (1767), pp. 103–123.

  8. C. F. Gauss, Disquisitiones circa superficies curvas, Typis Dieterichianis, Goettingen, 1828.

  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.

  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.

  11. Felix Klein, Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade, Teubner, Leipzig, 1884.

  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.

  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.

  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.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bogdan D. Suceavă.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Suceavă, B.D. A Geometric Interpretation of Curvature Inequalities on Hypersurfaces via Ravi Substitutions in the Euclidean Plane. Math Intelligencer 40, 50–54 (2018). https://doi.org/10.1007/s00283-017-9766-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00283-017-9766-2

Navigation