Dergiler / International Electronic Journal of Geometry / 2019 / Cilt: 12 - Sayı: 1

A Characterization of Cylinders and an Estimate for Mean Curvature of Convex Euclidean Hypersurfaces Satisfying a Cylindrical Condition

Sayfa
57–60
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We show that a curvature condition on the Gauss-Kronecker curvature and scalar curvature of a

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Amaç & Hipotez:We show that a curvature condition on the Gauss-Kronecker curvature and scalar curvature of a
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Temel Bulgular & Veri:We show that a curvature condition on the Gauss-Kronecker curvature and scalar curvature of a
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Sonuç & Katkı:We show that a curvature condition on the Gauss-Kronecker curvature and scalar curvature of a
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:principal curvatures · mean curvature · scalar curvature

Abstract

We show that a curvature condition on the Gauss-Kronecker curvature and scalar curvature of a

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Bu Makaleye Atıf Yap

GIUGIUC, L. M., SUCEAVA, B. D. (2022). A Characterization of Cylinders and an Estimate for Mean Curvature of Convex Euclidean Hypersurfaces Satisfying a Cylindrical Condition. International Electronic Journal of Geometry, Cilt: 12 - Sayı: 1, 57–60. https://ajindex.com/articles/539640

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Kaynakça (19)

  1. Bonnet, O., Sur quelque propriétés des lignes géodésiques. Comptes rendus de l’Academie des Sciences 11 (1855), 1311–1313
  2. Brubaker, N.D. and Suceava, B.D., A Geometric Interpretation of Cauchy-Schwarz Inequality in Terms of Casorati Curvature. Intern. Elec. J. Geom. 11 (2018), 48–51
  3. Brubaker, N.D., Camero, J., Rocha Rocha O., Soto, R. and Suceav˘a, B.D., A Curvature Invariant Inspired by Leonhard Euler’s Inequality R ≥ 2r. Forum Geometricorum 18 (2018) 119–127
  4. Brzycki, B., Giesler, M.D., Gomez, K., Odom L.H. and Suceav˘a, B.D., A ladder of curvatures for hypersurfaces in the Euclidean ambient space. Houston J. Math. 40 (2014) 1347–1356
  5. Calabi, E., On Ricci curvatures and geodesics. Duke Math. J. 34 (1967), 667–676
  6. Chen, B.-Y., Some pinching and classification theorems for minimal submanifolds. Arch. Math. 60 (1993), 568-578
  7. Chen, B.-Y., A Riemannian invariant and its applications to submanifold theory. Results Math. 27 (1995), 17-26
  8. Chen, B.-Y., Some new obstructions to minimal and Lagrangian isometric immersions. Japanese J. Math. 26 (2000), 105-127
  9. Chen, B.-Y., Pseudo-Riemannian submanifolds, δ-invariants and Applications. World Scientific, 2011
  10. 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 J. Math. 17 (2013), 885–895
  11. Dillen, F., Fastenakels, J. and Van der Veken, J., A pinching theorem for the normal scalar curvature of invariant submanifolds. J. Geom. Phys. 57 (2007), no. 3, 833–840. [12] doCarmo, Manfredo P., Riemannian Geometry. Birkhäuser, 1992
  12. Galloway, G.J., A Generalization of Myers Theorem and an application to relativistic cosmology. J. Diff. Geom. 14 (1979), 105–116
  13. Gauss, C.F., Disquisitiones circa superficies curvas. Typis Dieterichianis, Goettingen, 1828
  14. Germain, S., Mémoire sur la courbure des surfaces. J. Reine Angew. Math. 8 (1832), 280–297
  15. Giugiuc, L.M., Problem 11911. American Mathematical Monthly 123 (2016), p. 504
  16. Myers, S.B., Riemmannian manifolds with positive curvature. Duke Math. J. 8 (1941), 401–404
  17. Suceav˘a, B. D., The spread of the shape operator as conformal invariant. J. Inequal. Pure Appl. Math. 4 (2003), article 74
  18. Suceav˘a, B. D., The amalgamatic curvature and the orthocurvatures of three dimensional hypersurfaces in E4. Publicationes Mathematicae 87 (2015), no. 1-2, 35–46
  19. Suceav˘a, B.D., A Geometric Interp