Homothetical Surfaces in Three Dimensional Pseudo–Galilean Spaces Satisfying ΔIIxi=λixi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta ^{II}\mathbf{x }_i=\lambda _i\mathbf{x }_i$$\end{document}

被引：0
作者：
Mohamd Saleem Lone
机构：
[1] Tata Institute of Fundamental Research,International Centre for Theoretical Sciences
来源：
Advances in Applied Clifford Algebras | 2019年 / 29卷 / 5期
关键词：
Homothetical surface; Finite type surface; Laplacian operator; Pseudo-Galilean space; Primary 53A35; Secondary 53B30; 53A40;
D O I：
10.1007/s00006-019-1007-7
中图分类号：
学科分类号：
摘要：
A homothetical surface arises as a graph of a function z=φ1(v1)φ2(v2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z = \varphi _1(v_1) \varphi _2(v_2)$$\end{document}. In this paper, we study the homothetical surfaces in three dimensional pseudo-Galilean spaceG31\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( \mathbb {G}_3^1\right) $$\end{document} satisfying the conditions ΔIIxi=λixi,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta ^{II}\mathbf{x }_i=\lambda _i\mathbf{x }_i,$$\end{document} where ΔII\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta ^{II}$$\end{document} is the Laplacian with respect to second fundamental form. In particular, we show the non-existence of any such type of surface in G31.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {G}_3^1.$$\end{document}
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