Wintgen Ideal Surfaces in Four-dimensional Neutral Indefinite Space Form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R^4_2(c)}$$\end{document}

被引：0
作者：
Bang-Yen Chen
机构：
[1] Michigan State University,Department of Mathematics
来源：
Results in Mathematics | 2012年 / 61卷 / 3-4期
关键词：
Primary 53C40; Secondary 53A35; 53C50; Inequality; Wintgen ideal surfaces; pseudo-hyperbolic 4-space; Gauss curvature; normal curvature; mean curvature;
D O I：
10.1007/s00025-011-0119-8
中图分类号：
学科分类号：
摘要：
For an oriented space-like surface M in a four-dimensional indefinite space form\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R^4_2(c)}$$\end{document}, there is a Wintgen type inequality; namely, the Gauss curvature K, the normal curvature KD and mean curvature vector H of M in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R^4_2(c)}$$\end{document} satisfy the general inequality: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K+K^D \geq \langle H,H \rangle+c}$$\end{document}. An oriented space-like surface in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R^4_2(c)}$$\end{document} is called Wintgen ideal if it satisfies the equality case of the inequality identically. In this paper, we study Wintgen ideal surfaces in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R^4_2(c)}$$\end{document} . In particular, we classify Wintgen ideal surfaces in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R^4_2(c)}$$\end{document} with constant Gauss and normal curvatures. We also completely classify Wintgen ideal surfaces in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb E^4_2}$$\end{document} satisfying |K| = |KD| identically.
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页码：329 / 345
页数：16
相关论文
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