2022年微分几何试卷试题答案及评分参考 .pdf

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1、20XX 年湖北省高等教育自学考试微分几何试卷试题答案及评分参考（B卷）（课程代号：2014 ）一、单项选择题（本大题共10 小题，每小题 1 分，共 10 分）1 2 3 4 5 6 7 8 9 10 D B C C D C A D A B 二、多项选择题（本大题共5 小题，每小题 2 分，共 10 分）11 12 13 14 15 ABDE BD AD ACD AC 三、填空题（每小题1 分，共 10分）16、17、018、019、)0,cos,sin(tt20、2/21、2dn22、大圆23、124、三内角之和小于等于25、)()()()(cabcbabcaabc以下分数是累计分四、简单

2、计算题（每小题4 分，共 20 分）26、)cossin3,sincos3(22ttttr1 分|cossin|3|ttr2分弧长为2/3cossin32/0tdtt4 分27、)1,cos,sin(ttr1 分0t2 分4 分28、2 分3 分4 分29、3 分64 分30、|/cosbaba1 分ba20ZY2222bdvadudvduIIIknbdvduadvdu221321021001),(cba文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5

3、A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B

4、1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H

5、4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6

6、W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z

7、6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F

8、7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1

9、J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4122/24 分五、综合计算题（每小题10 分，共 30 分）31、曲率公式3()trrr，挠率公式2(,)()tr rrrr 2 分(sin,cos,)at at br，(cos,sin,0)atatr，(sin,cos,0)atatr3 分22|abr4 分224|a barr6 分22aab，22bab10分32、设抛物面的参数表示为),(xyyxr，则),0,1(yrx，),1,0(xry，yyxxrr)0,0,0(，yxxyrr)1,0,0(

10、，)1,(1001xyxykjirryx1)1,(22yxxyn3 分21yE，xyF，21xG6 分0NL，1122yxM，6 分32211yxK8 分文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 H

11、O8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV

12、6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编

13、码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4

14、 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1

15、ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文

16、档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H43221yxxyH10 分33、因为0F，所以是正交网。2 分圆柱螺线是v-曲线，由刘维尔定理有1ln2vgG

17、kuE。5 分直接计算得221,EGua，8 分所以211avg。10 分六、证明（每小题10 分，共 20 分）34、（1）由222ng，如果曲线是测地线（0g）且是渐近线（0n），则0，所以曲线是直线。2 分（2）由伏雷内公式有。由于曲线是测地线，有n。综合这两个等式有n。5 分因为曲线是曲率线，所以是主方向，由罗德里格定理即ddnr，其中是主曲率。所以nn。8 分综合以上两个式子得n0，由此得0。10 分35、设曲面上曲线C：()(),()su s v srr，s是弧长参数，是C与u-曲线的夹角 则dcossincossind|uvuvuvsEGrrrrrrr。另一方面，由链式法则有dd

18、dddduvuvsssrrr。比较这两式得dsindvGs，ddcosdduuEss，4 分上 面 最 后 一 个 等 式 是 因 为1E。所 以 我 们 有dtandvGu，即文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:C

19、J6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO

20、8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6

21、H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码

22、:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4

23、HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 Z

24、V6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H41dtan()dvGu6 分将sin与cos的表达式代入刘维尔公式得d1ln1lnco

25、ssind22gEGsvuGEddG dvsuds。所以有1dddddtan()ddgGvGsvGvuuu。10 分文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8

26、F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A

27、1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8

28、M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10

29、X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ

30、6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4文档编码:CJ6A1J6W5A4 HO8R8M9Z6B1 ZV6H10X8F7H4