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.

¡ ¢ ¡ £¢¥¤§¦ ¡¤ 4¡'_5.734 ¦ 4 84:+@),+35a+32D%Y+%8! ; 4B0+5*'734B0+- D%8? $E@@+/U&+355#'%*7¤+-2 4V0¡E$5.!3L 734 5*' § %*L+-589Q%Y+-$06%*E$E@U,¢ 4V06%*) %*E"!G5 4HL+346)H>6/ +35 % ¤K ; !30P2H`++*+35; ; @)A58) %8E@E 5*'' ¢ ¦C¦ 46E@E7 ) 5§¦Z)N0:58)H!34(',L 46)H0¡4(5*'Z+32H4 >3 4:7-4:),+3"%*? $E$`+/U9Q%¦Z2 4:7-4C58' ¤K ; !-0P2 `++*]9Q% ; ; $).!M$!M+-2H%Y+¦'_587¦46%.0P2 ¦ +32 46734]$!%*E$9\5.!G+M46S84:7-U 9Q% ; ; @) §91£' 3 '¥)$¦Z2 "0P2N4(',LH%8E$!:/ 4:S.4:7-U ¦Z2H4:7-4C4HL 0¡4 ; +\58) %A!G4:+%8,¤¤4b0:%8) 84¡+ %*)\4(',L $SY%*E$4:),+ 0¡5.)H0¡4 ; +=58' 7-460¡+3¥D%*?H@E$`+/U¦@'*¦ 4Z+P% .4X+32 4#>4 H)H`+-@5.)Q5*'¦%*? $E@@+/U(%8?D5YS.4#%8)H>%8! Q@)H!G+34B%8>]+32D%Y+Z+32H4 B) !XE$@4[5.)C, !3L ? 9Q%*)H`'_5.E$> !:¢7-460+-!3$9¦$E"%*717-46%.!G5.) $) !32 5§¦R![+-2H%Y+ ¦ 4 0:%*) %8! A5.) E@U +-2H%Y+¦+32 4 ) !M?D4]+32H4¦84B!158'b!GL ?D!G4:+-!¦5*' '! L )D>4:7 ¤K ; !-0P2 `++*(9Q% ;H; @).! _$)H!G+346%.> 5*'a? @E$ ; !30P2H`++*$9\%; ; @),! ¢ 9Q%+ "! ) 5*+ 2H%*7P>\+35M?D46E@$4:S.4R+-2H%Y+X734B0+- D%8? E$4b!G4:+-! 2H%WS84R+-%*)84:),+ ; E$%8) 46! %*E$9\5.!G+¤¤¤¤¤¤< § 4B>>JI¤£¤¤4 ,)H5§¦ +32H%*+b%*E$9\5.!G+X%8E@E ; 58$),+-!X5*' ($)%¦0:58L ),+P%*? E$4a)H0:4¦) $58) 5*'H, 9\%8) @'_58E"> !¦`+C"!¦) 5*+C!35 !3L 7 ; 73"!3@)A+32D%Y+C% ; ; 735 L$9\%*+34(+-%*)84:),+P!L¤¤¤¤¤¤¤$ ¦ £¢¥¤ ¢ ¦¢ £ £ ¢ ©!¢ ¢ £"# £+¤£©¨4:S.4:7-U ¦Z2 4:7-4X'_587='_L )H0+-@5.)H!:¢ + $! %@¦X%WUM58'O!3%WU$)&+32D%Y+ %*+ %*E$9\5.!G+ %8E@E ; 5.@),+-!=+32H4!34¡+R?4:2H%WS.46!¦ 46E@E%8E@9\5.!G+XE@ 84F%¦4:LD0¡E$$>4B%*)! ; %80¡4,¢E@4:+LH!?H%80[L ; %8)H>H) @+3$58)*¢&%L ; ; 5.!34F+-2H%Y+6¦ 41+-% .4[+32H40¡5.)H!3$>467a!3589\4F9\587-4F?H%.!G"0[9Q%Y+3+3467-!a5*'>44 H) @+3$58) %8!#%*?5YS84M4HL 0¡4 ; +&+32H%*+6¦ 4¦734 ; E$%.0¡4M+32 4\7-4(',L $73469\4:),+b+-2H%Y+&+32H4!-%*9\4¦>) !1?D4(? @E$ ; !30P2H`++*C4(',L $SY%*E$4:),+F+35A!GL ?D!G4:+-![58''!9¦Z@+32 +32H4(7-4(',L $73469¦46),+[+32H%*+?H!34¡+P!5*'-, !3L ? 9Q%8) `'_5.E$>H! _58'> @9\4:)D!G$58) 5*' '*)5¢ X2 4:)!¦ 4 ¦ 58L E">+32H4:U¦?D4b!3L84:+ %*)(4(',L $SW%8E@46),+ >4 D) `+-@5.)*¢ X2H%Y+ 9Q%WU¦!34:469(?UQ0¡5.L ),+-%*?HE@4#L ) $58)H! 587X?H%.>C!34¡+-!5*'D9¦4B%8!3L 7-4@*:46735@)\!GLD0P21%&¦X%WU#+32H%*+ +-2 4X4:7-735.7 !34¡+P!^> 5b) 58+7-46%8E@E$U&9Q%Y+G+-4:7^@)M+32H44:)D> ¢A%@9\$E$%873E$U +32 4 ; 58$).+P!a%*+6¦Z2H$0P2V+-2 4\>¡ 4:7-4:),+-$%8E^58' §2D%8!a7-%8) E@4B!3!b+32H%8)%*7-4 ; 5*+346),+3"%*E$E@UV?H%.>? L+#+32 4¦$9\% 84M5*'+-2 $!#!34¡+&L )H>467 §V2H%.!b9\46%.!GLH734A*64:7-5%*)D>C!G5 ¦ 4a9\%WUM'_58784:+ %8?D5.L+ @+=+-5,5 ¢ § 7-5892 4:7-4R@+ "! ) 5*+ +35512H%87->¦+-5M!34:4b+32H%*+4:S.4:7-U ¦Z2 4:7-4%Y+ E$46%.!/+ @) !G5.9\4a!34:)H!34©¢ X2 4#LH!GLD%*E) 5*+-@5.)C5*'+P%*).4:),+ ; E"%*)H4a>546!) 58+"¦ 5.7 F2H4:7-4¦Z2 46734Z5.) 4 +-% 846!% ; 58$),+EDC$) %8)H>\%8! !^+-2H%Y+=%8E@E ; 5.@),+-!58) ) 4B%*7¡D¦E$$4 S.4:7-U&0:E@5,!G4=+35a+32 4 +-%8)846),+ ; E"%*)H4?460:%8LH!34 ¦ 4 %8734 %*E$E@5§¦Z$)a0:58L ),+P%*? E$4L ) $58)D!1%*)D>N%*7-? @+37P%*7-UA!34¡+-!15*'R9\46%.!GLH734*64:7-5¢ 9\ 82,+¦0:58),+-%8@)N%¨0:58L ),+P%*? E$4>46)H!G4R!34¡+'_5.7@)H!G+-%8)H0¡45.7%[0¡58LH).+P%*? E$4Z>4:)D!G4X'%89¦$E$U15*' E$`+3+3E$4R!GL 73'%80:46!:¢ )¦+-2 $!9\46%.!GL 7-47 +32H4:587-4¡+-$0=!G4:+G+3$)a58) 4 2H%8!O+35¦ 5.7 6¦Z`+-2F+-2 4 0:58)H0:4 ; +^5*' #-% ; ; 7-5 L@9Q%*+34+-%8)846),+ ; E"%*) 4B!%$) ¦Z2H$0P2F5.) 4 > 4:9Q%*)H>H!K+-2H%Y+^9¦5,!/+ ; 5.@),+P!O$) )H46%*7FDME$$4=S84673U¦Z2H4:7-4 #39\5.!G+0%#$!0:589 ; L+-46>¦$)M+-4:7-9Q!5*' ?b%8LH!3> 5870¡E$5.!34 +35&+-2 4X+-%8)846).+ ; E"%*)H49\46%.!GL 7-4©¢E%464< §D%*E>%8)H>=< G¨%*+G+-@E"%> ¢4HL"!/+%*E$9\5.!G+^46S84673U ¦Z2 46734,¢ X2 4X9Q%*$) ; 58$),+"! +35#?D4R06%*7-4¡'_L E%8?D5.L+ +-2 4X9\46%8!3L 7-4

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

Saved successfully!

Ooh no, something went wrong!