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Journals / International Electronic Journal of Geometry / 2018 / Cilt: 11 - Sayı: 1

A Geometric Interpretation of Cauchy-Schwarz Inequality in Terms of Casorati Curvature

Nicholas D. BRUBAKER
Bogdan D. SUCEAVA
Pages
48–51
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In a visionary short paper published in 1855, Ossian Bonnet derived a theorem relating prescribed

📌 3 Key Takeaways

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Objective & Hypothesis:In a visionary short paper published in 1855, Ossian Bonnet derived a theorem relating prescribed
📊
Key Findings & Data:In a visionary short paper published in 1855, Ossian Bonnet derived a theorem relating prescribed
💡
Conclusion & Impact:In a visionary short paper published in 1855, Ossian Bonnet derived a theorem relating prescribed
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:principal curvatures · Casorati curvature · smooth surfaces

Abstract

In a visionary short paper published in 1855, Ossian Bonnet derived a theorem relating prescribed

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Cite This Article

BRUBAKER, N. D., SUCEAVA, B. D. (2022). A Geometric Interpretation of Cauchy-Schwarz Inequality in Terms of Casorati Curvature. International Electronic Journal of Geometry, Cilt: 11 - Sayı: 1, 48–51. https://ajindex.com/articles/539656

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References (8)

  1. Bonnet, Ossian: Sur quelque propriétés des lignes géodésiques, Comptes rendus de l’Academie des Sciences, 11 (1855), 1311–1313
  2. Calabi, Eugenio: On Ricci curvatures and geodesics, Duke Math. J., 34 (1967), 667–676
  3. Casorati, Felice, Mesure de la courbure des surfaces suivant l’idée commune. Ses rapports avec les mesures de courbure gaussienne et moyenne, Acta Math. 14 (1) (1890), 95–110
  4. Chen, Bang-Yen, Geometry of submanifolds, M. Dekker, New York, 1973
  5. Chen, Bang-Yen, Geometry of submanifolds and its applications, Science University of Tokyo, 1981
  6. Chen, Bang-Yen, Pseudo-Riemannian submanifolds, -invariants and Applications, World Scientific, 2011. [7] doCarmo, Manfredo P., Riemannian Geometry, Birkhäuser, 1992
  7. Galloway, Gregory J., A Generalization of Myers Theorem and an application to relativistic cosmology, J. Diff. Geom., 14 (1979), 105–116
  8. Myers, S. B., Riemmannian manifolds with positive curvature, Duke Math. J., vol. 8 (1941), 401–404.