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...

You also want an ePaper? Increase the reach of your titles

YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.

¡ ¢ ¡ £¢¥¤§¦ ¡ ) < #%WS %4:9?> ¤£ %b0:58)S8467-!34"¦X%8! 58?+P%*$) 46>"!B¦ 4:E$EZ?4:2H%WS.46>¤¤¤$ $)H0¡E$LH>$) !3589\4C58'X+32 4]58) 4B![9\4:),+3$58) 4B>¦X%WU!=0:58),+-%8@) 4B>Q$)]!34¡+-!¦Z2 "0P2(%.>9\`+Z% ; %*7P%*9\4¡+-4:7-*B%Y+3$58)Q58'K+32H4b+/U ; 4a$)%*7-4a%8Ea%WS">>¡£ £¡ ¢ 4:7a%C734 8L E"%*7Z9Q% ;H; @)C$!bL ) @'_587-9\E@U 734B0+- D%8? E$4©¢ +a"!R) 58+©) 5§¦Z) ¦Z2 4¡+-2 4:7L) @'_587-9\E@U]734B0+3¥D%8? E@4[!34¡+Z"!R0¡5.).+P%*$) 46>]$)!3LH0P2%¦734 8L E"%*7X$9\% 84,¢4:S.4:7-UQL"!!G@+3LD%Y+3$58) ; 7-5YS$> 46!%#) $0:4Z4HL %*9 ; E$4X5*'2 5§¦ 9\4¡+-73"0Z>5.L ? E$@)&9\46%.!GLH734B!X2¤¤' ¤ ¨ #D ¤¥¤ "!¦!3L C0¡$4:),+-E@UN0:E@5,!G4(+35 ?D46@) 4:LD0¡E$$>4B%*)*¢ 5.),S.4:7P!G46E@U¤¤¤¤¤¤¦ £¢¥¤ ¢ ¦¢ £ £ ¢ ©!¢ ¢ £"# £+¤£©¨L )H`'_5.739 E@5§¦ 4:7&?58L )H>H![58)A+35 ; 5.E@5 8U ¢ 5V58+32 467[9\4¡+32H5> "! ) 5§¦Z)+346739Q!&58'58$)\+32 "!Z$)2 .2 4:7R0:5>@9\46)H!G$58)D!¢ ¦b)H%*E$U,+3"0:%8E9¦4:+32 5> !a%8!X$)0< %469?> ¢ ¤£'_587R>+-5!¦ 5.7 QS.4:7-U!¦ 46E@EK$)2 82 467X0:5>@9\46)H!G$58)D!¢>5\) 58+b!G464:9+-5R+-2 4X4 460+^+32D%Y+`'U858L12H%WS84=%8)¦R2HÈ '_5.7-!&7-4.L E$%87[!G4:+F58) ¦Z2 "0P2 !3L C0¡$4:),+3E$U 9Q%8),UA!G$)8LHE$%87[@),+34 87P%*E5 ; 4:7P%Y+-587P!+-2 4:) +32 4V!34¡+Q91LD!/+\?D4L )H`'_5.739\E$UN734B0+- D%8? E$4©¢ %5.9¦458+32 4670P2H%87-%.0+34673 *6%*+3$58)H!6¦ 4:7-4Q46!G+-%8? E@"!32 46>¢X2 4B!G4#7-46!3L È +P!X!G2 5§¦ 46>Q+32H%*+ +-2 4:7-4¦ %.!=7-46%8E@E$U\58) E$UQ58) 4#)H%*+3L 7P%*E) 5*+-@5.)46%873E$$4:7L ) @'_587-9 7-460¡+3¥D%*? $E$`+/U,¢ + ¦X%8!&%8E$!35V!G2 5§¦Z) +32H%*+FL ) @'_587-9\E@Ü 7-460¡+3¥D%*?HE@4Q!34¡+-!5*'§ 5.79\587-4@)'_5.739Q%*+3$58)[%*?58L++-2 46!34+35 ; "0:!K!34:4 < a%WS %4:9?> ¢¥§¦ X%8)H>< %4:9?> ¥ ¥ ¢¢ ¦ ¢¡ ©¡ ¨ ¤ £¤ © © ¢ ¦ ¥ £¤ §¥¤ ¥D £¢ " A ¤ 8#D ¤¥¤ ¦ ¨ ¤ §¦ ¤ ¤ © ¦ £ § ¨ ' ¦ /=1 A 3 ¨ ¤ ¢ ¦! ¥¤¦¤ ¨ ¨©¨ / ¨ ¦ ¦ , ¨A ¨ ¨ ¨ $ ¨¨ ¨ $¤¦¤ , £¦ ¦ ¦ ¨¦ ¨ / 1§' 3 ' >4 H)H46>?UC/ D D $!b734 8L E"%*7 ¢ ¦ ? @E$ ; !30P2H`++*4:9M?D4B> >$) $!#7-48LHE$%87b@' A $!&>5.L ? E$@)? L+[7-48LHE$%87b9Q% ; ; @),!b)H4:46> ) 5*+&?4$E@ ; !-0P2 @+*©¢ 5*+-4a+-2H%Y+R%M734 8L E"%*7 9Q% ; ; @)\0:%8)]2D%WS84b5.) E$U(%1?58LH)H>46>])L 91?4:7?; 7-4:$9Q%84B! '_587Z46%.0P2 ; 58$),+Z@) +32H4[7-%8)84,¢5*'8L E"%*7¦9Q% ; ; $),! ; 735YS">4]LD!¦Z`+-2 %ASY%*7-$%*+3$58) 5.)N+-2 4 +32 469¦458'¦Z2H%*+Z4855> ; %*7P%*9\4:+34:7- *6%Y+-@5.)*¢ )H!G+34B%8>V58'%.! $)Q+-2H%Y+&%(!34¡+a%.>9\`+&%0¡5.)H!G+3@+3L+-46!#%? $E@ ; !-0P2 @+* ; %87-%89¦4:+34673 *6%*+3$58)C?U(%\46LH0¡E$$> 46%*)! ; %80:4; %87-%89¦4:+34673 *6%*+3$58)¦Z2 "0P2 %*E$E@5§¦R![!3589\4Q0¡7-5.!-!3@),!¢ 4C0¡5.L E$> %*E"!35%.! ¨+32H%*+1%8$S846)¦!34¡+?4R0¡5.).+P%*$) 46>M$)\%#7-4.L E$%87@9Q%.4X5*'%#46LH0¡E$$> 46%*)\! ; %80:4>¢ 4,¢¦ 4Z0:58L E">%*E$E$5§¦'_587X+-2 4F!3% 84#5*'?H%*E"%*)D0¡4©¢!G5.9\4#2H58E$46!a4 D) `+-@5.) ¢ 0:%*)T?D4 LH!346>%.!]% ¦ %WU +-5 ; 4:73+3L 7-? 46LH0¡E$">46%8) 846589\4¡+-73U D ¤¤ 9\5>46!G+3E$U©¢ (K4¡+ ?4A%N9\4:+37-$0A>58L ?HE@$)N9\46%.!GLH734¨5.) '!%*)D> E@4:+ ¨>46) 5*+-4F+32H4M%8!-!350:$%*+34B>'.LD%8!3$>"!G+-%*)D0¡4¦Z@+32 ¢ +b+3LH73)H!%8!b@) ¢ ¥¢ 58L +^+-2H%Y++-2 4X@9Q%.4 58' ' ¤ ¨#D ¤¥¤ $) '¥)]L )H> 4:7%#734 8L E"%*7^9Q% ; ; $)#$!%8E ¦X%WU!/; 7-5 ; 4:73+/U158'9\4¡+-73"0R>5.L ? E$@)L ) @'_587-9\E@U¦7-460+- %*? E$4©¢ X2 "!=0¡5.9\46!'_7-589 +32 4 §¦Z2 "0P2 2 46E ; !M+-5A46)H!GLH734(+32H%*+M+-2 4 .4:5.9¦4:+37-U 5*'9\46%.!GL 7-46!X2H4:587-4:96¢¢ 8$S84:) %

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

Saved successfully!

Ooh no, something went wrong!