張佳欣,胡娜,姜楊
四維Minkowski空間中偽零曲線(xiàn)的伴隨曲線(xiàn)
張佳欣1,胡娜1,姜楊2
(1. 沈陽(yáng)工業(yè)大學(xué) 理學(xué)院,遼寧 沈陽(yáng) 110870;2. 沈陽(yáng)師范大學(xué) 數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院,遼寧 沈陽(yáng) 110034)
定義了四維Minkowski空間中偽零曲線(xiàn)的伴隨曲線(xiàn).利用偽零曲線(xiàn)的特殊性,將歐氏空間中曲線(xiàn)的性質(zhì)擴(kuò)展到偽歐氏空間.通過(guò)對(duì)偽零曲線(xiàn)及其伴隨曲線(xiàn)的Frenet標(biāo)架的討論,給出不同類(lèi)型伴隨曲線(xiàn)的曲率函數(shù)表達(dá)方式.討論了特殊曲線(xiàn)的伴隨曲線(xiàn)的曲率函數(shù),并給出相應(yīng)實(shí)例.
Minkowski空間;偽零曲線(xiàn);伴隨曲線(xiàn);Frenet標(biāo)架;積分曲線(xiàn);曲率函數(shù)
文獻(xiàn)[1]在三維和四維歐氏空間中定義了Frenet曲線(xiàn)的一類(lèi)伴隨曲線(xiàn),并給出這類(lèi)伴隨曲線(xiàn)的一些特征以及與初始曲線(xiàn)曲率之間的關(guān)系.本文研究了四維Minkowski空間中偽零曲線(xiàn)的伴隨曲線(xiàn),根據(jù)不同類(lèi)型曲線(xiàn)的特征以及不同F(xiàn)renet標(biāo)架之間的關(guān)系,得到伴隨曲線(xiàn)的一些性質(zhì),并給出實(shí)例.
對(duì)式(2)做內(nèi)積,可得
隨著時(shí)代的發(fā)展,微分幾何學(xué)科也逐漸被重視,各類(lèi)型曲線(xiàn)的伴隨曲線(xiàn)也被各界人士所研究,特別是偽零曲線(xiàn),本文定義并討論了四維Minkowski空間中偽零曲線(xiàn)的伴隨曲線(xiàn),定義了積分曲線(xiàn)作為偽零曲線(xiàn)的伴隨曲線(xiàn),根據(jù)不同類(lèi)型曲線(xiàn)的Frenet標(biāo)架的計(jì)算,得到伴隨曲線(xiàn)的曲率函數(shù).與文獻(xiàn)[1-13]中對(duì)于這種類(lèi)型的曲線(xiàn)研究相比大有不同,并且呈現(xiàn)的結(jié)果更為清晰,為今后微分幾何中這種類(lèi)型曲線(xiàn)的研究提供了有益的計(jì)算經(jīng)驗(yàn).
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Associate curve of pseudo null curve in 4-dimensional Minkowski space
ZHANG Jiaxin1,HU Na*,JIANG Yang2
(1. School of Science,Shenyang University of Technology,Shenyang 110870,China; 2. School of Mathematics and Systems Science,Shenyang Normal University,Shenyang 110034,China)
The associate curve of the pseudo null curve in 4-dimensional Minkowski space was defined. The properties of curves in Euclidean space are extended to pseudo-Euclidean space by using the particularity of pseudo null curve. By discussing the Frenet frame of the pseudo null curve and its associate curves,the expression of curvature functions of different types of associate curves were given.The curvature function of the associate curve of a special curve is discussed,and some examples were given.
Minkowski space;pseudo null curve;associate curve;Frenet frame;integral curve;curvature function
1007-9831(2023)07-0018-04
O186
A
10.3969/j.issn.1007-9831.2023.07.005
2022-11-04
張佳欣(1998-),女,遼寧朝陽(yáng)人,在讀碩士研究生,從事微分幾何研究.E-mail:zhangjiaxin9919@163.com.
胡娜(1985-),女,遼寧沈陽(yáng)人,講師,博士,從事微分幾何研究.E-mail:huna19850208@hotmail.com.