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

©{¡ " §¢¡¡ ¡ £ ¢¡ £¥§© ©ƒj©¡ ¤ " © ©V§A §6 ¡ ¡J£ £¢ © ! ¡ Dp©K$&E'D25*¤&e,$K£&4$=a*I&.4£2x=F??A$BD' X (i/)K¤/DK$&]=^(+&BD,$(+4£'(¡(Q$a2>'(>&/f254£GI/DK$&e68B;2>?g/;25-^/DB)&.&"W '0/D2>B0/D(i4Q$ X (i/)K £3}pc © 4£'0/)&.2aG[=>6}/;2(^(+45$=^=x-+&¨/¦A£'/DB)J/D=xK£2rC>&ƒ-i&9')'¦')J^*¤*I&/)BDJ=>6 ?=>,$(+&.'ƒ=56Y/)K$&'D25*¤& G£4$(i/)&')&¨/ W -i&/ A}' A£'0&2¤')&9¡A$&4}?¨&M=56254p(+4/G£4$(i/)&,$BD=FGFA£?¨/¢ £ ¨ ¤ W &92>?;K X (7/DKj2*¤,$-+( ?2B;GF&.B%] ?¨=>*¤(+45$I68B)=a* /)K£&,}&.B)*AF/D25/)(+=>4£';_gc/)=¤H$BD&.2z(3/)K£&`'0J^*¤*¤&¨/)BDJ3/DK£2BDG /D=\')&&/)K£25//DK$&p4$& X Ca&B;'0(+=>4"=>6 £ }'D2rJ=56 /)K$& £ ¨ ? ' (+'eA£4$(768=aB)*¤-+JqH%=>A$4£G$&.G c"=56&-+&*¤&.4a/;'*[A£?;K X &92(>&.B[?¨=aA£')(i4j=>6E'0&.-76?.K$&pGF=>A$H£-i(+45$\?=>4£G$(7/D(i=a4„?2>4jH}&p'0&.&4„2a'2© 4£'0/)&.2aG„=>6M'D2rJ^(i45$ /)K£25/3/)K$&'),£2>?&-i=^=z(F'/)K£& ')2>*I&2-i-'D?2>-i&9'')(i*¤(+-+2>B)(i/:J>cW /)K$&pGF=>A£H$-i(+45$Z?¨=>4}GF(7/D(i=a4j')2rJF'`/)K£25/“$>&.=>*¤&¨/DB)(+&.'/)K£25/=F??A$B25/254}G"-i=F?.24}'2 H}=aA$4£GF&9G"6 25*¤(+-iJac " K$(+'GF('&%&.B)&.4¡/¤'D?2>-i&9'[254}Gj-+=^?.24Q$ W (i4„/)K$&,$BD&.?¨&9GF(+45$ &XLF2>*¤,$-i& X &p?¨=aA$-+G„?¨=>45.H%=>A$4£G$&.GF4$&9')'(=>B /DK$&x68BD2a?g/;25-s/)BD&&')=I/)K$&.J25BD&M4$=5/E')=3'0&.-76?. '0(+*¤(i- 25B9c$a2a'(a&¨/X §%2(>&68A£4£?g/D=>BYG$=¡&9' 4$=>/ GF( '0/)A$BDHx/)K$&ƒ'0&.-76?. ')(i*¤(+-+2>B)(i/:JE,$BD=>,5.;=>/)&¦/DK£2/)K$&.B&B)/)(+&.'Y/DK£2BD* /)K$&$a&=a*I&/)BDJ3=56*¤&¨/)BD( ?M'),£2a?¨&.'.cXGF&9')?B)(+H}&9G2>H}=c*¤&¨/DB)( ?' , ] E4'M(+4 ] Oc 3 c83z3r_gc %&3?2>4Z'0/)(+-+-I$>&¨/,$-+&4¡/:J =>61( '0=a*¤&¨/)BD(+&.' X (7/DK=>H$/D25(+4$&9GI68B)=a*/)K£&E'0&9¡A$&4£?& ¢ £ ¨ ¤ X (+-i-}H}&MGF=>A$H£-i(+45$(i6 2>4£G¤=>4£-iJI(76s/DK$&4^A$*[H%&B'0/)BDA£?g/254p(+4a/D&BD&.'0/)(+45$¤'0,£2a?¨&M68BD=>*2>4¡J3H%=>A£4£GF&.G')&9¡A$&.4£?¨&M=56,}=¡'0(i/)(+C>&M(+4a/D&X$a&B;'3 ] /)K$&?25B;GF(+4£25-+(i/)(+&.'ƒ=56 /)K$& £ ¨ ? 'D_¨c =^&-i6?. '0(+*¤(i- 25BD(7/:J X =aA$-+G?=>BDB)&9'0,%=>4£Gk(i4p/DK$(+'‹?¨=a4£'0/)BDA£?g/D(i=a4k/D=I,%&BD(+=^G$(+?')&9¡A$&.4£?¨&9'c25BD-iJ X & ?¨=>A£-+G[*I=FGF(i68J/DK$&e?¨=>4}':/DB)A£?¨/)(+=>4£'Y=56}/)K$& =^(+&BD,$(+4£'(¡(F?.25BD,}&/2>4£G=^(+*¤(i- ¦ ¢ §yqR$4u!o # kxVJjs5sq4kaJrs s$#{tZkaJ¡yq{u¦s5k xVJ ¥Xkao$ s 4s pJdspq t4Jjv,§ k x s2¥Fö §}#s J¡§wxVJ ¥Xk Qq !2o;Jds k §ƒt{q3+¥FsMs$#{t!2o;Jjx s$# #Psqk¤v s CJrsp§wvK$&ƒ4$&HL^/¦GF&HG}4$(7/D(i=a4,£B)=