[幾何] Regular Surface

看板Math作者TampaBayRays (坦帕灣光芒)時間13年前 (2013/01/12 23:27)推噓2(2推 0噓 2→)

留言4則, 2人參與討論串1/1

Let x =f(v),z=g(v) a<v<b f(v)>0 be a parametrization for a rugular plane curve C. Let S belong to R^3 be the set obtained by rotating C about z axis. Show the parametrization of S and prove that S is a regular surface. 請問他的參數化是x(u,v)=(f(v)cos u,f(v)sin u,g(v))嗎? 我知道要證regular surface 要證他可微,一對一,跟homeomorphism 可是課本上說可微跟1-1很簡單可是我不會所以想請問各位大大如何證明他是regular surface 謝謝!!! -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 220.136.71.234

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turboho

01/13 16:06, , 1^F

01/13 16:06, 1^F

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turboho

01/13 16:07, , 2^F

01/13 16:07, 2^F

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herstein

01/13 16:35, , 3^F

01/13 16:35, 3^F