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Hypersurfaces with Lr-Pointwise 1-Type Gauss Map

Hypersurfaces with Lr-Pointwise 1-Type Gauss Map

In this paper, we study hypersurfaces in Еⁿ⁺¹ whose Gauss map G satisfies the equation LrG = f(G + C) for a smooth function f and a constant vector C, where Lr is the linearized operator of the (r+1)-st mean curvature of the hypersurface, i.e., Lr(f) = Tr(Pr ○∇²f) for f ∊ C∞(M), where Pr is the r-th...

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Main Author: Akram Mohammadpouri
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2018
Series:Журнал математической физики, анализа, геометрии
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/145859
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spelling irk-123456789-1458592019-02-02T01:23:12Z Hypersurfaces with Lr-Pointwise 1-Type Gauss Map Akram Mohammadpouri In this paper, we study hypersurfaces in Еⁿ⁺¹ whose Gauss map G satisfies the equation LrG = f(G + C) for a smooth function f and a constant vector C, where Lr is the linearized operator of the (r+1)-st mean curvature of the hypersurface, i.e., Lr(f) = Tr(Pr ○∇²f) for f ∊ C∞(M), where Pr is the r-th Newton transformation, ∇²f is the Hessian of f, LrG = (LrG₁, . . . ,LrGn₊₁) and G = (G₁, . . . ,Gn₊₁). We focus on hypersurfaces with constant (r + 1)-st mean curvature and constant mean curvature. We obtain some classification and characterization theorems for these classes of hypersurfaces. У статтi вивчаються гiперповерхнi в Еⁿ⁺¹ гауссове вiдображення G яких задовольняє рiвняння LrG = f(G + C) для гладкої функцiї f i постiйного вектора C, де Lr є лiнеаризованим оператором (r + 1)-ої середньої кривизни гiперповерхнi, тобто Lr(f) = Tr(Pr ○∇²f) для f ∊ C∞(M), а Pr є r-им перетворенням Ньютона, ∇²f є гессiаном f, LrG = (LrG₁, . . . ,LrGn₊₁) i G = (G₁, . . . ,Gn₊₁). Наша увага зосереджена на гiперповерхнях з постiйною (r+1)-ою середньою кривизною i постiйною середньою кривизною. Для цих класiв гiперповерхонь отримано теореми класифiкацiЁ i характеризацiї. 2018 Article Hypersurfaces with Lr-Pointwise 1-Type Gauss Map / Akram Mohammadpouri // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 1. — С. 67-77. — Бібліогр.: 23 назв. — англ. 1812-9471 DOI: https://doi.org/10.15407/mag14.01.067 Mathematics Subject Classification 2010: 53D02, 53C40, 53C42 http://dspace.nbuv.gov.ua/handle/123456789/145859 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description In this paper, we study hypersurfaces in Еⁿ⁺¹ whose Gauss map G satisfies the equation LrG = f(G + C) for a smooth function f and a constant vector C, where Lr is the linearized operator of the (r+1)-st mean curvature of the hypersurface, i.e., Lr(f) = Tr(Pr ○∇²f) for f ∊ C∞(M), where Pr is the r-th Newton transformation, ∇²f is the Hessian of f, LrG = (LrG₁, . . . ,LrGn₊₁) and G = (G₁, . . . ,Gn₊₁). We focus on hypersurfaces with constant (r + 1)-st mean curvature and constant mean curvature. We obtain some classification and characterization theorems for these classes of hypersurfaces.
format Article
author Akram Mohammadpouri
spellingShingle Akram Mohammadpouri
Hypersurfaces with Lr-Pointwise 1-Type Gauss Map
Журнал математической физики, анализа, геометрии
author_facet Akram Mohammadpouri
author_sort Akram Mohammadpouri
title Hypersurfaces with Lr-Pointwise 1-Type Gauss Map
title_short Hypersurfaces with Lr-Pointwise 1-Type Gauss Map
title_full Hypersurfaces with Lr-Pointwise 1-Type Gauss Map
title_fullStr Hypersurfaces with Lr-Pointwise 1-Type Gauss Map
title_full_unstemmed Hypersurfaces with Lr-Pointwise 1-Type Gauss Map
title_sort hypersurfaces with lr-pointwise 1-type gauss map
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate 2018
url http://dspace.nbuv.gov.ua/handle/123456789/145859
citation_txt Hypersurfaces with Lr-Pointwise 1-Type Gauss Map / Akram Mohammadpouri // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 1. — С. 67-77. — Бібліогр.: 23 назв. — англ.
series Журнал математической физики, анализа, геометрии
work_keys_str_mv AT akrammohammadpouri hypersurfaceswithlrpointwise1typegaussmap
first_indexed 2023-05-20T17:23:16Z
last_indexed 2023-05-20T17:23:16Z
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