Recent Developments in Wintgen Inequality and Wintgen Ideal Submanifolds

Bang-yen CHEN

doi:https://doi.org/10.36890/iejg.838446

Makale detayları

Recent Developments in Wintgen Inequality and Wintgen Ideal Submanifolds

Yazarlar:

Bang-yen CHEN

Yayıncı:

Kazım İLARSLAN

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Geometry 2021 Vol.14 Issue 1, pp.6-45

Belge Tipi:

Makale

Yayın Tarihi:

4/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000471562

Sıklık:

İki Yıllık

eISSN:

1307-5624

DOI:

https://doi.org/10.36890/iejg.838446

Özet:

 


P.  Wintgen proved in [Sur l’inégalité de Chen-Willmore. C. R. Acad. Sci. Paris 288, 993–995 (1979)] that  the Gauss curvature GGG and the normal curvature KDKDK^D of a surface  in the Euclidean 4-space E4E4E^4 satisfy G+|KD|≤∥H∥2,G+|KD|≤‖H‖2,G+|K^D|\leq \Vert H\Vert ^2, where ∥H∥2‖H‖2\Vert H\Vert ^2 is the squared mean curvature. A surface M2M2M^{2} in E4E4E^4 is called a {Wintgen ideal} surface if it satisfies the equality case of the inequality identically. Wintgen ideal surfaces in E4E4E^4 form an important family of surfaces; namely, surfaces with circular ellipse of curvature. In 1999, P. J. De Smet, F. Dillen, L. Verstraelen and L. Vrancken  gave a conjecture for Wintgen inequality on Riemannian submanifolds in real space forms, which was well-known as the DDVV conjecture. Later, the DDVV conjecture was proven by Z. Lu  and by Ge and Z. Tang independently.In this paper, we provide a comprehensive survey on recent developments in Wintgen inequality and  Wintgen ideal submanifolds.

.

Makale detayları

Recent Developments in Wintgen Inequality and Wintgen Ideal Submanifolds

Yazarlar: Bang-yen CHEN

Yayıncı: Kazım İLARSLAN

Ana Başlıklar: Matematik

Dergi: International Electronic Journal of Geometry 2021 Vol.14 Issue 1, pp.6-45

Belge Tipi: Makale

Yayın Tarihi: 4/2021

Belge Dili: İngilizce

Document ID (Org No.): 2000471562

Sıklık: İki Yıllık

eISSN: 1307-5624

DOI: https://doi.org/10.36890/iejg.838446

Sayı

Yazarlar:

Bang-yen CHEN

Yayıncı:

Kazım İLARSLAN

Ana Başlıklar:

Matematik

Dergi:

International Electronic Journal of Geometry 2021 Vol.14 Issue 1, pp.6-45

Belge Tipi:

Makale

Yayın Tarihi:

4/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000471562

Sıklık:

İki Yıllık

eISSN:

1307-5624

DOI:

https://doi.org/10.36890/iejg.838446