13.07.2015 Views

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

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

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

SHOW MORE
SHOW LESS
  • No tags were found...

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

& ¦ K$&1,}=a(i4¡/YK£&BD&f(+'@/)K}2*¤&.4a/9cK$&[G$=>A$H$-+&[')A$*n(i4 ] Oc c ) _ 2>?¨/)A£2>-i-+Jp?=>4^C>&.B ä&.' 25H}'0=a-iAF/D&-+J W H$AF/O=a4$&`?2>4¦¨ ¢¨¨ ]91 _ -¨¨' H}=aA$4£GF&9G X &0¨>&/ ] Mc c & _gc4$=a4e^&.B)=/)&.B)*3'e(= X -i&/`A£'?;K$&.? 5 ] Mc c Qa_gc | &/ 1 ¢© ( ¢ H%&-ä(iCa&4 W 254£G\-i&/`A£'x&.'0/)(+*32BD* =>6E/DK$& (c) W :A£'0/f/DK$&eH£2>')( ?1,£B)=a,}&.B0/D(i&9'=56£/DK$&(+Bv')(^.& W ')A$,$,%=>B)/ W 254£G | (+,£'D?;K$(i/^e4$=aB)*3'.cMc] Mc c Q>_gc4Z&`GF=¤4$=5/4$&.&.G/)K£&(+GF&.4¡/)(i/:JK£25/pGF=^&.' | &*¤*32 Mc c) *¤&.2>4£¢ _ =h4$=>//;265>& (7/;',£B)&9?¨( '0& 68=>BD* /D=^=4W /)K$&O,}=a(i4¡/ (+'v*¤=>BD&e/)K$&©¨>&.4$&B;25-$/:J¡,%&E=>6@?¨=a4£':/DB)A}?g/)(+=>4¤/DK£24¦*¤2>4$4$&.B¤')=Z-i=a4¨"2>' X & ¨>(+C>&/)K£&* H%=>A£4£GF&.Gh?¨=^& ;3?(i&.4¡/D'.c ¦ K$( '¤(+'25BDH$(i/)B;25BDJX K£25/B)&.*325B 5r2>H$-+& W &.C>&4(i6f(7/O(+'E4$=5/ECa&BDJkGF( ;q?¨A$-i/E/D=q,$BD=&>c ©†/O'D2rJ^'e/)K£25/')=>*¤&-i=F?.24}'2>B)& 25,$,£B)= LF(+*¤25/)&.-iJh(i4}GF&,%&4£G$&4¡/=56[&92>?;K/)K£&\CA£'p')?.25-+&.'p254£G¨¨¨¨¨¨¨¨¨¨¨¨ 9I¦9B9¡ ! ¢ " £¡ ¤£¦% ¢-¢e¦ "¢3¢-¦¢ ¤£$9¤ =a-+GF&.B ?=>4¡/)(+4^A$=>A}' 68A$4£?¨/)(+=>468=aB 2>4^JM?;K$=a(+?&=56¡ ¨ ¤ X K£2'¦(i/1( '¦H%=>A$4}GF&.G c 4Z&E')K£25-+-}GF( 'D?¨A£'D'/)K£(+'f68A$B0/DK$&B(+4a/D&BD,$BD&¨/1(i/e2>' 2[')A$*£B;':/ƒ(i4 %W (i4 X K$(+?;K25-+-%H£AF/}4$(7/D&-+J3*3254^J¤/)&.B)*3'1Cr2>4$( '0K W254}Gq/DK$&4 2¤')A$*(+4 ¦}c 3 ¨¦ = ,$BD=&3/DK$&-+&*¤*32 X &')&¨/S ¨ ]%1 _Il ¡¢ ©¢ ¨¢ ¢ ¨ ]%1 _ W 2>4£G X &/)BDJ\/)=\2>,$,$-+J ¦ K£&=>BD&*Mc c c 4\&K£2rC>&¤/DK£2BI25-+- ¦Z254}G }W254}Gp')=S ¨ ]%1 ¡ _vl 68=>BE2>-i- ¦ W 2>4£G'0= ] Oc c _v68=a-i-+= X 'c | &¨/A£'E?;K$&.? 5 ] Mc c & _gc ©†6l $W /)K£&4 &(i/)K$&.B 1 ( , ]$ 3 _O=aB 1 ¡ ( , ]$ 3 _ W 2>4£G (+4\&.(7/DK$&B`?.2>')&/)K£(+'?.254K£2>,$,}&.4p68=>B=a4$-iJ2¤H}=aA$4£GF&9G4^A$*H}&.B=56 f '.c b (+4£?& ¨/;265a&.' C4£'0/D2>4a//D(i*¤&9' 3 ¨ ¨¢ ¢ ¨w S ¨ ]%1 _ " S ¨ ] ©F_ w c ( =>/)( ?¨&[/)K£25/ ¢ ¨ ]91 _ " ¢ ¨ ] ©$_l ¨ ]%1 _ " ¨ ] ©$_ W 254£G/)K£25//)K£(+' ¥¡A£2>4¡/)(i/:J[( '4$=>4e^.&BD=M68=>B¦=>4£-iJI2OH%=>A£4£GF&.GI4^A$*H}&.Bf=56 f '¦22ä25(+4 c4K$&43(i/f(+'4$=a4e^&.B)=x(i/v(+'fH}=aA$4£GF&9G¤H¡J . 3 ¥¨,%]%1 ©$_ W H¡J | &.*I*32 Mc c & c ¦ K^A£' X &?=>4£?-iA£G$&/)K}2- GF&B¤?¨=a4¡/)(+4¡A£=>A£'`68A$4£?g/D(i=a4„=a4 ¢ =56E=aBDG$&B¢1c ¦ K$( '[,$BD=&9'254}GjGF&#}4$&.'¤2¨¨§f '3G$=¡&9'34$=>/¤*325/0/)&.B¤68=>B | &*¤*32©†/e/D&-+-+' A}' /)K£25/ X &?.254pH$A$(+-+G ¢ ¤ =a-+G$&B?¨=a4¡/)(+4¡A£=>A£'ƒ68A$4}?g/)(+=>4}' X (7/DKA£'ƒ/D=3*¤225>&ac25,£,$B)= LF(+*32-i&p254£G„-i=F?.24@c¦ K$(+45`=>6 ¢ ¨ 2>'H%&(+4¨'0=a*¤& 5^(+4£GI=56%H$A$*¤,I68A$4£?g/D(i=a4I/)K£25/-+(+C>&.'4£&.25B ( ¦ ] 3 ¨_254}G X K$(+?;K-+(+C>&.'E2(iBE/)=k'D2rJ3/DK£2&9'4$&925B F25-i/)K$=aA¨>K ¨]$ 3 _ W /)K$( '14$&&9G¤4$=5/ƒH}&e/DB)A£&E=56 ¢ ¨ WM( 'ƒ'0A$,£,}=aB0/D&.G¤(+4 ,H%&.?2>A£')&k=56(i/D'IGF&/£4$(i/)(+=>4] Mc c)Q>_gc ¢= X &Ca&B W /DK$&k=a4$-iJ"GF( '0/)A$BDH£254}?¨&q/D= /DK$(+'( 'M'0/D25/)&.*I&.4¡/M( '/DK$&¤2>G$GF(i/)(+C>&¤?¨=a4£'0/D254¡/ " ¨ ]%1 ¡ _ W X K$(+?;K\,$- 2rJ^'O=>4£-iJ2*I(+4$=aB/)&9?;K$4$( ?2>-OBD=>-+&>c ¦ K£(+'kH$A$*¤,68A$4}?g/)(+=>4 (+'4$=5/p4$=>BD*325-+(^.&.Gh/D=„K£2rCa& H}=aA$4£GF&9G¢ ¤¢ ¢ ¨( 'I,$BD=>,%&BD-iJ 4$=aB)*325-+( ^&.G c=a-+G$&B3?¨=a4£':/;254¡/[68=aBI/)K$&p&HLF,%=>4$&.4a/ ¢ W H$AF/ 3 ¨

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!