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

,%] E4/$>&¨/2I*¤&¨/DB)('e=>,%&B;2&O68A$4£?g/D=>BH%&.?.25A£')&(i/E(+'E25425H£'0/)B;2>?¨/K$(=>6f/)K$&6 25*¤(+-i( 25B?=>4£'0/)BDA£?g/D(i=a4£'O=561')4$= X §}2z(>&?A$BDC>&.'O(+4 /)K£&I,£-+2>4$&>c'© 4/.C>&.BD')(+=>4X §%2(>&e?=>4£'0/)BDA£?g/D(i=a4£'I$a(iCa&?¨A$BDC>&9' X K$( ?;Kq25BD&eH$(i-+(+,£')?;K£(7/¨7GF&.&.GI/)K£&O'0/D254}G$25B;G¤'04$=X §}2z(>&ƒ68A$4£?¨/)=>B125,$,$-+(+&.G/)=[2?(iB;?¨-+& =>Bf-+(+4$&'0&F$>*¤&4¡/ ] X (7/DK&9¡A$(+Cc § 4£&&9¡A$(+-2>?&.'/DK$&*¤(+G£GF-i&/)K$(+BDG¤=>6 &.2>?;K¤=>6%/DK$&e/DK$B)&.&E')(+GF&9'¦=562S N X (i/)Kk2x,£2>(iBv=56/)K£&43BD&,$-X K$( ?;K3,}=a(i4¡/v=aAF/D')(+G$& S N W ')=`2>'¦/)=`*32(a&2'0(+*¤,$-+&')&X$>*¤&.4a/;'¦=56s/DK$&E'D25*¤&e-i&.45$5/DK§ X K$( ?;Kk( 'f/DK$&OA£4$(i=a4k=>6 / X &.-iCa&E')&X$>*¤&.4a/;'v=>6@&9¡A£2>-}-+&4Q$5/)K@c § 4£&?¨-+=a')&.Gk?¨A$BDC>&]S¨')&X$a*I&.4¡/D'=>6f-i&.45$5/DK ¥¨/)(+*I&9'/DK$&[-+&4Q$5/)K =56¦/)K£&C¡C¡¡< ] Mc 3 c _¢X 2rJE/)K£25/Y&.A£?¨-+(+G$&.254$a&=a*I&/)BDJE( ' 4£25/)A$B;25->68=>B /DK$&1'0/D2>4£G$2>BDG | 2>,$- 2>?¨( 254@c/)K£&1'D25*¤&X -+&¨/¤£ H}&x2[G£4$(i/)&x')&¨/ X (i/)K2?&(K£&4 ¢‹ 3 X &xG$=?¨&M=56 ¢r_gc ," K$&x*¤=a'0/16 2>*¤=>A£' ')4$= X §}2(a&O?A$B)Ca&O( '1/)K$&&m¦=a4-Ox=F?;K2I'0A$(i/D2>H$-+&x?;K£=>(X §}2(a& W}X K$(+?;K\(+'O=>H$/D25(+4$&9G(i4 /)K$&68=>-+-i= X (+45$q*32>4$4$&B9c § 4$&'0/D2>B0/;' X (i/)K 2>4')4$=/)K£&4hB)&.,}&924„/)=Z,$BD=^G$A£?¨& ¡ =>B;G$254„?A$BDC>&.' S O4£')( ':/D(i45$k=56 § DN c " K£&m¦=>4 Ox=^?;K3')4$= X §}2z(>&e( 'v=aHF/D2>(i4$&9G32>'f/)K$&O-i(+*¤(7/ƒ=56 /)K£&S ¨? ' ] (+4')(+GF&9'f=>6ƒS¢E25A}')GF=aBe&/D=>,%=>-+=C$aJ¤68=>B?¨=a*¤,£2>?¨/e')&¨/;'D_¨c //)K£&;=>/)&v/)K£25/ ] ¢i< ,}] EA$H£-i(+45$£c+ '2OC4`=a4`/)K£&1/DK$&*¤& =56%'04$= X §%2(>&9'Y?=>4£')( GF&B 4C§ X (i/)K`/DK$& *¤&¨/)BD( ?GF&XG£4$&.GpH^J,}] E6ƒE(+44C¦c " K$( 'ƒ'0,£2a?¨&( 'ƒGF=>A$H£-i(+45$£cX K$&.B)&]E;sGF&4£=5/)&9'f/DK$&E,%=>(+4¡/ ] E § < ) ) )6¦£¤c .M(+C>&.4q/ X =`&-+&*¤&.4a/;'}El ¢E ¢ ¤ }2>4£GF¤l ¢F>¢ ¤ }=56§£ } 254£Gp2I4¡A£*[H%&B S ] 5< 3 /@'0&/, ] E4¢ 68=>B X ¥ ¦p?¨//)K$&9'0&q2>B)&P/D V S)N ÀbV S _!Ë TgW@X K$( ?;K"*¤&.2>4£'ƒ/)K£25/, ] E4