Metric Structures for Riemannian and Non-riemannian Spaces M ...

] '¥)Y_ W H$AF/M(7/E( 'O(i46 2a?g/OH%=>A£4£GF&.G=a4(+'p25- X 2rJF'q'),%&.?¨( 25-W /DK$& $=aA$BD(i&.B¦/)B;254£'068=>BD* W &/D?5c ¦ = ¨>=x/D=H%&.?2>A£')&=56%/)K$&¢(+-iH%&B)/1'),£2>?&E'0/)BDA£?g/DA$B)&¦k'),£2>?&.'O(i4 /)K$( 'x?¨=a4a/D&HL^/O=a4$&IK£2>'E/)=?¨=a*I&[/)=/)&.B)*3' X (7/DKZ')=>*¤&)ä&=a*I&/)BDJ>c _£K$&9'0&=>,%&B;26¦/)K$&.(iB05>&.B)4£&- ' W =>4$&IK£2a'/D=q/D225>&(i4¡/)=2>?.?¨=aA$4¡/E/)K£&:A£'0/M(+4K$&.B)&`2>B)&`2>4£25-+=2äA$&.' =>6 /DK$&.')&`=a,}&.BD25/)=>B;' =>4 '*),+3§q2>'D'0=F?(+25/)&.G/D=3/)K$&[K$&.25/¦=56 /)K£& ¤@2>,$-+2a?¨( 254 W 68=>B X K$(+?;K /DK$&q,£2>BD2>H}=a-i( ?¤*¤&¨/DB)( ?qGF&/£4$&.'=>,%&B;2B(+4£'0/)&.2aGäKa/ ä&=a*I&/)BDJ>c ¦ K$&BD&[2>B)&`2>-+')=q254£2>-i= ¨>=aA£' =>,%&B;2B;' =>4/)K£& ¢&.(+')&4^H%&B ¨/)K£&[BD(#)')A$H!] ¤@25,£-+2a?¨( 254&%k/)K$&.B)&ac § 4 =>A$BI'0J^*[H%=>-+( ? 254¡/)=aB¨>BD=>A£,ZA}'0(+4¨/DK$&q4£25/)A$B;25-' ¨>&.4$&B;25-%/:J^,}& W *325B)/)(+4ä2>-i&O/)B;254}':68=aB)*3'.c=>,%&B;2B;'ƒ=56@/DK$(K$&9'0&`'),}&9?¨( }?x=>,%&B;2B;'eGF=34$=>/K£2rC>&2542>H£':/DBD2a?g/e68=aB)*o=>4'0,}2>?¨&9' =56¦K$=§]¦/:J^,%& W H$AF/f/DK$&BD&25BD&e4£2A$- 25Bf(+4¡/)& ¨>B;25-F=>,%&B;2B;'*¤=2ä&4$&.=>A£'K$( ?;Kq(+4£?¨-+A£GF&E/)K$&9'0&&XL$25*¤,$-+&.'v2>4£G X K$( ?;Kk?.2543H%&OGF&/£4$&.Gq=>4k'),£2>?&.'¦=>6 K$=>*¤=§]X¦ K$( ' X 2>'M=>4$&¤=>6v/)K£&I*32>(i4Z*¤=5/)(+C- '0&/0/)(+4¨}c/)K£&`':/DA£GFJk=>6&/ ] ¢0 ]91 ¢©$_# %@_ H%&f2e'),£2>?&¦=56^K$=>*¤=2ä&4$&.=>A£'%/:J^,%& W 254£Gx-+&¨/ §¡( £ § ¢324 ] ¢ %@_¤%), ]%1 5_0_ ¨ … ]%), ]%1 5_0_ ¨ … ]] c c)r_]91 5_( 'k/DK$& 2 ! N U R-i- , ]%1 5_ W /)K$& 2rC>&.BD22¨>&*¤=X K£(+?;K §GF&.C¡( 2&.BD22¨>&x=>4 /)K£25/OH£2>-i- c § 4$&I?2>4/)K$(+4525*¤=aA$4¡/OH^JX 2rJ\/)=Z*¤&.2a'0A$BD&k2\'04£2>,£')K$=5/[=>6 §sc © 4j/DK$( '')&.?¨/)(+=>4„2>4£G /)K£&4$&XL^/=56(i/32>'I2X = X & X 254¡/E/D=-+=^=252BM=56/] $=>Bx4$=>/D25/)(+=>4£2>-')(+*I,£-i( ?¨(i/:J X &¤G$=p4£=5/*3265>&/)K£&¤G$&,%&4£GF&.4£?¨&3=>61*¤= ]91 5_§sc§k&XL^,£-i( ?¨(i/ W H£AF/(7/E')K$=aA$-+Gp25- X 2rJ^'ƒH%&`?¨-+&.2>B168BD=>* /)K$&`?=>4¡/)&XL^/.c _=>4¡ ¢ £¢¥¤§¦¢¡¡+£©¨ ¦ £¢¥¤ ¢ ¦¢¤££ ¢ !©"¢£¢#£$% £ & /)K}24 ££ ¦ X K$&.4P)¦¥ 7§¥ ¥ W 2>4£G 4$=>/ X K$&.4 7 l )2 ¥c ] £?2>4£?¨&.-i- 2&B;')(i=a4p=>6 W H$AF/M/)K£&BD&25BD&['0/)(+-i-')&¨/=>/)&IK$= X &C>&.BE/DK£2?&[=56fK£=>*¤=2ä&4$&.=>A£' /:J^,%&>c © 4 ,$B;2>?¨/)( ?¨&[/)K$&I(i4¡/D&BD&.'0/)(+4¨2B;'=a4=>,%&B;2B;'Y?=>*¤&ƒ68B)=a*/)K£&e,£25B)/)( ?¨A$- 25B¦'),£2>?& W /DK$& ¨>&.4$&B;25-¡/)K£&=>BDJ`')(i*¤,$-+J[25,£,$-i(+&.'/)=I/DK$& X K$=>-+&`?¨- 2>'D'ƒ=56=>,%&B;2B;' X (i/)K$=aAF/OGF( '0/)(+4¨>A$( ')K$(i4¨¤?&B)/D2>(i4p=>4$&9'c¥ §©¨¤@¤§}#¥ A # ¡A¦¥ ¤$# §¤$# §¦ §A¨¨¤2¥ A §%#¡H%& ¨>(+C>&4@c b &¨/w § ] ©$_ " * ¨ …§ w % ] ©$_ *¤= ]91 5_ƒlX K$&.B)&* ¨ … §3l§ ] _ % ] _ ¦ ] c c 3 _