mini di manifold - colorado state universityclayton/teaching/diffg... · 2015-04-08 · mini case...
TRANSCRIPT
Mini case an Differentiable Manifold & brass manias
÷pt .
Mathemhh notebookan
"
is views f the hyprspke"
÷smarmily :
Thespare of k - dim 't liner shspmes of IR
" 1 or a ) is called the Gasman in f k - plans in R"
lei ) & dented
GEHR ") tr 6th , D or Gln , e) or ... )
frqmmnins shop in : . ttgdm geometry - poet Witf first as Rlmd in conty problems,
so . . .
. Combinator icsnsesp .
Schubert Globo,uhh us developedto aow posts He " How may
Has in
3 -
sparektsut 4 glen lines ?
"
. Different geometry- door easels f tongues spas ,
uhih are gnolnb f Lie gaps ,ad f Spas
w/ posilm Ricci curate
. Applied meth - . sign Attn. blind Sore sgnalm
. opfmzath ( liner & qndhlnostninb pt yuan a bass mmnin ... e.g. , symmemezewknpoh .)
.clued random way & polymer moody
.etc
.
Gyi . GHRD B the spare f lnythfhtheo Dm in R?. . so a gy f RP ¥5
. 6,1N) is Mph & me gulf G, ( R
" ) = RIP "
. Gz 1123=6 ,R 3
Also,
on thik f 6 dR3 as the space f all Imes in Mph
. 62112" to at to be a gyf 5×5 ?
. 6 ,¢
'
= ep'
I 5
←goal is to buildup smef the they needed to talk abut these spaces
Df: A diftemtstkmnifld of dims inn is a Hansdorft,send onttde tpdogil space M together wl a family f inject 't
meps Ha : Ua ER"
→ M of gusts Us c- IR"
st. :
a Y UalUD = M
@ Far my xp st. UalUH n Ypl Up) = Wt 0 ,
the sb Uj'
lw) & Ypilw) are gusts in Rn & the
mps yj'
olla & Uj'
olfs are smooth 1 8).
𐀀𐀁𐀂𐀃𐀄𐀅𐀆𐀇𐀈𐀉𐀊𐀋𐀍𐀎𐀏𐀐𐀑𐀒𐀓𐀔𐀕𐀖𐀗𐀘𐀙𐀚𐀛𐀜𐀝𐀞𐀟𐀠𐀡𐀢𐀣𐀤𐀥𐀦𐀨𐀩𐀪𐀫𐀬𐀭𐀮𐀯𐀰𐀱𐀲𐀳𐀴𐀵𐀶𐀷𐀸𐀹𐀺𐀼𐀽𐀿𐁀𐁁𐁂𐁃𐁄𐁅𐁆𐁇𐁈𐁉𐁊𐁋𐁌𐁍𐁐𐁑𐁒𐁓𐁔𐁕𐁖𐁗𐁘𐁙𐁚𐁛𐁜𐁝3𐀀𐀁𐀂𐀃𐀄𐀅𐀆𐀇𐀈𐀉𐀊𐀋𐀍𐀎𐀏𐀐𐀑𐀒𐀓𐀔𐀕𐀖𐀗𐀘𐀙𐀚𐀛𐀜𐀝𐀞𐀟𐀠𐀡𐀢𐀣𐀤𐀥𐀦𐀨𐀩𐀪𐀫𐀬𐀭𐀮𐀯𐀰𐀱𐀲𐀳𐀴𐀵𐀶𐀷𐀸𐀹𐀺𐀼𐀽𐀿𐁀𐁁𐁂𐁃𐁄𐁅𐁆𐁇𐁈𐁉𐁊𐁋𐁌𐁍𐁐𐁑𐁒𐁓𐁔𐁕𐁖𐁗𐁘𐁙𐁚𐁛𐁜𐁝 the family { 1Ua,Ua)} is mnxinl w
.H .
𐀀𐀁𐀂𐀃𐀄𐀅𐀆𐀇𐀈𐀉𐀊𐀋𐀍𐀎𐀏𐀐𐀑𐀒𐀓𐀔𐀕𐀖𐀗𐀘𐀙𐀚𐀛𐀜𐀝𐀞𐀟𐀠𐀡𐀢𐀣𐀤𐀥𐀦𐀨𐀩𐀪𐀫𐀬𐀭𐀮𐀯𐀰𐀱𐀲𐀳𐀴𐀵𐀶𐀷𐀸𐀹𐀺𐀼𐀽𐀿𐁀𐁁𐁂𐁃𐁄𐁅𐁆𐁇𐁈𐁉𐁊𐁋𐁌𐁍𐁐𐁑𐁒𐁓𐁔𐁕𐁖𐁗𐁘𐁙𐁚𐁛𐁜𐁝1𐀀𐀁𐀂𐀃𐀄𐀅𐀆𐀇𐀈𐀉𐀊𐀋𐀍𐀎𐀏𐀐𐀑𐀒𐀓𐀔𐀕𐀖𐀗𐀘𐀙𐀚𐀛𐀜𐀝𐀞𐀟𐀠𐀡𐀢𐀣𐀤𐀥𐀦𐀨𐀩𐀪𐀫𐀬𐀭𐀮𐀯𐀰𐀱𐀲𐀳𐀴𐀵𐀶𐀷𐀸𐀹𐀺𐀼𐀽𐀿𐁀𐁁𐁂𐁃𐁄𐁅𐁆𐁇𐁈𐁉𐁊𐁋𐁌𐁍𐁐𐁑𐁒𐁓𐁔𐁕𐁖𐁗𐁘𐁙𐁚𐁛𐁜𐁝 &@.
+500¥µuk y§
' 1W)#"
#R "