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Dergiler / International Electronic Journal of Geometry / 2018 / Cilt: 11 - Sayı: 2

A Ladder of Curvatures in the Geometry of Surfaces

Nicholas D. BRUBAKER
Jasmine CAMERO
Oscar Rocha ROCHA
Bogdan D. SUCEAVA
Sayfa
28–33
Yayın Tarihi
2018-11-30
DOI
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Many investigations in the local differential geometry of surfaces focused on Gaussian curvature

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Amaç & Hipotez:Many investigations in the local differential geometry of surfaces focused on Gaussian curvature
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Temel Bulgular & Veri:Many investigations in the local differential geometry of surfaces focused on Gaussian curvature
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Sonuç & Katkı:Many investigations in the local differential geometry of surfaces focused on Gaussian curvature
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:principal curvatures · Gaussian curvature · mean curvature

Abstract

Many investigations in the local differential geometry of surfaces focused on Gaussian curvature

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Bu Makaleye Atıf Yap

BRUBAKER, N. D., CAMERO, J., ROCHA, O. R., SUCEAVA, B. D. (2018). A Ladder of Curvatures in the Geometry of Surfaces. International Electronic Journal of Geometry, Cilt: 11 - Sayı: 2, 28–33. https://ajindex.com/articles/672089

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Kaynakça (16)

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  2. Chen, Bang-Yen, Total mean curvature and submanifolds of finite type, World Scientific, 1984
  3. Chen, Bang-Yen, Pseudo-Riemannian geometry, δ−invariants and applications, World Scientific, 2011
  4. Brzycki, B.; Giesler, M.D.; Gomez, K.; Odom L.H.; and Suceava, B.D., A ladder of curvatures for hypersurfaces in the Euclidean ambient space, Houston Journal of Mathematics, 40 (2014). pp. 1347–1356
  5. Conley, C. T. R.; Etnyre, R.; Gardener, B.; Odom L.H.; and Suceava, B.D., New Curvature Inequalities for Hypersurfaces in the Euclidean Ambient Space, Taiwanese Journal of Mathematics, 17 (2013), 885–895
  6. Decu, S.; Haesen, S.; and Verstraelen, L., Optimal inequalities involving Casorati curvatures, Bull. Transylv. Univ. Bra¸sov Ser. B 14 (2007), 85–93
  7. Decu, S.; Haesen, S.; Verstraelen, L.; Vîlcu, G.-E., Curvature Invariants of Statistical Submanifolds in Kenmotsu Statistical Manifolds of Constant -Sectional Curvature, Entropy 20 (2018) 20, 529. [8] do Carmo, M.P., Riemannian Geometry, Birkhäuser, 1992
  8. Euler, Leonhard, Recherches sur la courbure des surfaces, Memoires de l’academie des sciences de Berlin (written in 1760, published in 1767), 16: 119 –143
  9. Gauss, C.F., Disquisitiones circa superficies curvas, Typis Dieterichianis, Goettingen, 1828
  10. Germain, Sophie, 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
  11. Kenmotsu, Katsuei, Surfaces with Constant Mean Curvature, translated by Katsuhiro Moriya, Translations of Mathematical Monographs, Vol. 221, American Mathematical Society, 2003
  12. Knoebel, Art; Laubenbacher, Reinhard; Lodder, Jerry; Pengelley, David, Mathematical Masterpieces: Further Chronicles by the Explorers, Undergraduate Texts in Mathematics, Springer-Verlag, 2007
  13. Spivak, Michael, A Comprehensive Introduction to Differential Geometry, third edition, Publish or Perish, 1999
  14. Suceava, B. D., The spread of the shape operator as conformal invariant, J. Inequal. Pure Appl. Math, 4 (2003), issue 4, article 74
  15. Suceava, B. D., The amalgamatic curvature and the orthocurvatures of three dimensional hypersurfaces in E4, Publicationes Mathematicae, 87(2015), no. 1-2, 35–46
  16. Suceava, B.D., A Geometric Interpretation