Journals / International Electronic Journal of Geometry / 2023 / Cilt: 16 Sayı: 2

Classification of Codazzi and Note on Minimal Hypersurfaces in $Nil^{4}$

Pages
707–714
Publication Date
2023-10-29
DOI
—
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AI Summary & Key Takeaways

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

We also give a characterization of a class of minimal hypersurfaces in $(Nil^{4},\widetilde g)$ with an example of a minimal surface in this class.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we give a classification of Codazzi hypersurfaces in a Lie group $(Nil^{4},\widetilde g)$.
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Key Findings & Data:In this paper, we give a classification of Codazzi hypersurfaces in a Lie group $(Nil^{4},\widetilde g)$.
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Conclusion & Impact:We also give a characterization of a class of minimal hypersurfaces in $(Nil^{4},\widetilde g)$ with an example of a minimal surface in this class.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Codazzi hypersurfaces · minimal hypersurfaces. · nilpotent Lie group

Abstract

In this paper, we give a classification of Codazzi hypersurfaces in a Lie group $(Nil^{4},\widetilde g)$. We also give a characterization of a class of minimal hypersurfaces in $(Nil^{4},\widetilde g)$ with an example of a minimal surface in this class.

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Cite This Article

DJELLALI, N., HASNİ, A., CHERİF, A. M., BELKHELFA, M. (2023). Classification of Codazzi and Note on Minimal Hypersurfaces in $Nil^{4}$. International Electronic Journal of Geometry, Cilt: 16 Sayı: 2, 707–714. https://ajindex.com/articles/971856

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References (8)

  1. Belkhelfa M., Dillen F., Inoguchi J.: Surfaces with parallel second fundamental form in Bianchi-Cartan-Vranceanu spaces. Banach Center Publishing, 57, 67-87 (2002)
  2. Calvaruso G., De Leo B.: Curvature properties of four-dimensional generalized symmetric spaces. J. Geom. 90, 30-46 (2008)
  3. Filipkiewicz R.: Four dimensional geometries. PhD thesis, University of Warwick, Great Britain (1983)
  4. Hasni A.: Les géométries de Thurston et la pseudo symétrie d’après R. Deszcz. PhD thesis, University of Tlemcen, Algeria (2014)
  5. Lawson H.B.: Local rigidity theorems for minimal hypersurfaces. Ann. Math. 89, 187-197 (1969)
  6. Leo B.D., Veken J.V.: Totally geodesic hypersurfaces of four-dimensional generalized symmetric spaces. Geom Dedicata, 159, 373-387 (2012)
  7. O’Neil: Semi-Riemannian Geometry. Academic Press, New York (1983)
  8. Willmore T.J.: Riemannian Geometry. Clarendon Press, New York (1993).