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£2>,$,%&4 =a4$-+J68=aBM2H%=>A$4£G$&.G 4^A$*H}&.BO=>6 ( ¦ W H}&9?25A}'0&I=56 ¤@&*¤*32/)K£(+'x?2>4c c £c$=>Be&92>?;Kp=56Y/)K$&9'0& f ' X &xK£2rCa&O/DK£2-i(i/:JZ(+'I254$=>/)K$&.B`C4¡/[=56 ] c c )§)r_ W 254£Gj(7/¤?254"H%&G$&BD(iCa&.G¦/)K£&qGF&#£4£(7/D(i=a4 ] c c )9_E=56ƒ*¤= ]%1 & _M2>4£G/DK$&3GF=>A$H£-i(+4¨?¨=a4£GF(i/)(+=>4 =a4 %¦c68BD=>*4£?& X &\K£2rC>& ] c) c ) & _ X & ?.254 G$&BD(iCa& ] c) c & _I68BD=>* ] c ) c) a_¤2>4£G /)K£&§§ ( 3c2>'D')A$*¤,F/)(+=>4/)K£25/K$( 'e?¨=a*I,£-i&/)&.'ƒ/DK$&,$BD=^=56Y=>6¡¤@&*¤*32 c ) c 3 c¦K$&q,£B)&9?¨&.G$(i4¨\25B ¨>A$*¤&4¡/2>-+')= X =>B 5^' X K$&4 §\/D225>&.'[C*¤& '*) W¦ 254£2a?;K '),£2>?&>c ¦ K$( 'O=aH£')&BDCr25/)(+=>4 ( 'O,}=>/)&4¡/D(+2>-i-+JA£')&¨68A$-H%&.?2>A£')&=>BM&Ca&4\(i4Z2X 2>4¡/D' §pBD&.2>-i-+Jp/)=/D265a&[C*¤&¤'0,%&.?(+2>- ')&¨/ W -i( 5>&I2(+4\')=>*¤&?.2>')&.'O=>4$&] c ) c a_ 2>4£G ] c ) c & _ X &`K£2rCa&x/)K£25//)K£&LF(+*324}' § /;265a&IC-iA$&9'xC>&.B)J ?-i=¡'0&/)=p/)K£&q')2>*I&¤')&¨/ W 2'0/ X K$&4 25,£,$B)='I')*325-+- &4$=aA¨>K c ©†6O/)K$&pB;254ä&k=56 § ( '¤2 4£(+?&p')&¨/ W -+( 5a&2 £4$(i/)&,}=a-iJ^K$&9GFBD=>4(G W /)K$&.4 X &[?2>4,$B)=aH£25H£-iJpGF&¨68=aB)*n/)K£& § f 'M'0-+( ¨>K¡/)-+Jp')=k2a' /)=k/D265a&=>BM23*3254$(i68=>-4£GF&.B¤')A$(i/D2>H$-i&?=>4£GF(i/)(+=>4}' X &p?.254h25- '0= ¨>&¨/I/)K£&.')&C*I&')&¨/.cLF(+*324}'E/D=H}&3K$=a*¤=5/)=a,$( ?[/D=&.2a?;K\=>/)K$&.B W 25/`-i&92>'0/x68=>B`')*¤2>-i- c ¦ K$(+'25,£,$B)==>A$- GkA}'0&`2>-+')=[/DK$&A$4$( ¥¡A$&4£&.'D' B)&9'0A$-i/ ¤ &.*¤*¤2 c ) c QFcXK$&M,}=a(i4¡/ =56Y2>-i-%=56@/)K$( ' (+'v/)K}24$&M?2>4k4$=aB)*325-+-+JI&XL^/)B;2>?g/168B)=a* *325,$,$(+4¨¡'¦(i/)K CB/)K£&,$A£B),%=a')&k=>6&HL^/)B;2>?¨/)(+4¨ /D=>,%=>-+=2¨>( ?2>-v(+4F68=>BD*32&.B(+4'I=>4$-+J /)K$&pBD&.25-]†Cr2>B)( 25H£-i&k2a'0,%&.?¨/D'[/)K£25/I*325/0/)&.B.c b && T BD&^ ( (+B W168=>B¤*¤=>BD&(i/I(*¤2>,$,$(+4ä' X (i/)KqC6W &9'0,%&.?(+2>-i-+JkGF& ¨>BD&&O/)K$&.=>BDJ>c=a'D?¨(+-+-+25/)(+=>44h/)BDJ^(i4¨ /)K$&\?¨=>*¤,$A$/D2A$- G© /D="A$4£GF&.BD'0/D2>4£G=56 ¤ /)K£(i45xH£2a? -+=2¨ w 1w ¤ ¥ 5/D=e/)K$&1&HL$25*¤,$-+&.' 254£Gx(i/D' ?¨=¡'0(+4$&f2a' 68A$4£?¨/)(+=>4£'@=>4x/DK$&vBD&.2>-¤ ¤X K$(+?;K¤-+(i&e(+4 3c ¦ K$&9'0& 68A£4£?g/D(i=a4£'f25BD&e4$=>/v?¨=>4¡/D(i4^A$=aA£' W =>B¦&.C>&4¤H%=>A$4}GF&.G¤(+4-+(i4$&¤ &.*¤*¤2 c) c 3 ,$BD=c¨ 9I¦9B9¡ ! ¢ " £¡ ¤£¦% ¢-¢e¦ "¢3¢-¦¢ ¤£$9¤ w § ] ©$_ " * ¨ § w % ] ©F_ y:. *¤= ]%1 & _ ¦*3254$(i68=>- G W =>BE23*¤&/)BD(+?'),£2>?&>c $BD=>*2>'68=>B¤?¨=a4a/D(i4^A$=aA£'*¤2>,$,$(+4ä'.c!© £B;':/¤&4}?¨=>A£4a/D&BD&.G /DK$( '( GF&92 (+4(+4F68=>BD*324_ =aA¨>-W W '),}&9?¨( }?2>-i-+J ¦ K£&=>BD&* c =a43, c) =>6 T _ =>Aä- W†c ¦ K£(+'vB)&9'0A$-i/¨¡2rC>& /)K£&Tc 2>4$( '0K$(+4¨*I&9254 =¡')?(i-+- 24 X 2a'4$=>/O*¤&4!]4^A$*[H%&BMBD&¦¥¡A$(+B)&9G(i4¡/)&.B),£B)&/D2A¨>-W$(i4I,£25B)/¦H}&9?2>A£'0&ƒ/DK$&eGF&#£4£(7/D(i=a4K£2aG[4£=5/¦J>&/H%&&.4(+4¡/)BD=FGFA£?¨&9G/)(+=>4£&.G(i4/)=¤/DK$&.')&68A$4}?g/)(+=>4}'c + ' *¤=&9'ƒ/)K$&9'0&`2>,$,$BD= L^(+*32A£')&

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

Saved successfully!

Ooh no, something went wrong!