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.

& ) ¥ ¤b 4:4C%*E"!35 b 4B0+-@5.) ¢ & )©¢ +["![S84673UV$9 ; 5.7G+P%*),+&2 4:7-4¦+32H%*+ ¦ 4 5) 5§¦ ¢ ) ¨¢ ?46! ¥£¢@+R$!X)H5*+Z+37-L 4#+32D%Y+ ¢ ) ¨¥¢ $9 ; E@$46!Z!3589\4:+32 $)¨\E@ 584! ¢ ) ¨¢ '_587R%8E@EK0:L; %87-%*+346E@U,¢'_587Z4B%80P2¡5L46>0¡LH?D4F!34+&$![%8E$!35($9 ; 5.7G+P%*),+#2H4:7-41+-2H%Y+&+32H4\0:58)H!G+-%8),+-!a@) ¢ ) ¨¥¢ >4 ; 4:)D> H)D%*E$E@U¤) ¥ ¦ 2 "!V>546!) 58+ ¥,L `+-4 ; 7-5YS84 ¦ 2 4:5.73469 ¢) ¨¥¢ )¤¤¤¤¤58+3"0¡4 +32D%Y++32H4 ¥,LH%.!G"!3U,9\9\4¡+-73UF0:58)H> `+-@5.)¦"!) 58+> $!G+3L 7-?46>¦?U10¡5.9 ; 5.!3$)¨(; ; $)¨¦Z@+32C%[>$E$%*+3$58)*¢ ¦R)UM46!G+3$9\%*+34B!+32H%*+"¦ 4R06%*)\2 5 ; 4X+-5 ¨84¡+'_5.7+32H4+32H4R9Q%5*'a>"!G+-%*)D0¡46!¦?U ¥,LH%.!G"!GU9\9\4¡+-73"0C9Q% ;H; @)¨.!¦2H%8!M+-5A7-46! ; 4B0+\+32D%Y+:¢>"!/+-5873+3$58)2 "!X0¡587-7-46! ; 5.)H> ! ) $0:4:E$U\+35¦+32H4b'%.0+X+32H%*+X+32 4 §/0¡5.)H>@+3$58)("! ) 5*+R>"!G+3L 7-?D4B>¦+- ; E$U@)¨\+32 4@¦ 4: ¨82,+Z?U(%¦91L E@+3 ; E$$06%Y+3$S84F0:58)H!G+-%8),+:¢?UC91LHÈ4&9\ ¨.2,+ ¦ 58)D>4:7¦Z2 4:+32 467 ¦ 2 4:5.73469 ¢) ¨¥¢ )a2D%8!R0:58L ),+3467 ; %*73+-! '_587Z58+32 467a)"0P2\+32 4b'_587-91L E"%Y+-@5.)\5*'+32H4b!/+P%Y+-4:9\4:),+ !G+3$E$EH9Q%65.46!!34:)H!34 ¦Z`+-2Q+32 4a9\46%8!3L 7-4¦Z27-5YS$>4B>1$) _ 4/H) @+3$58) ¢ ¨ ; E"%WU@)¨&+-2 4Z7-58E$4 58' ¤O4:?46! ¨8L 4Z9\4B%8!3L 734 ¢ + >546!3) f +;¦ 587 5Z'_587 %*),+35.7K!G4:+-!¤/¤¤?HL+O@+^>546!*¦ 5.7 5b'_587O%ZE$5*+ 5*'5*+32H4:7 ! ; %.0¡46!:¢ ¦N0:73@+34673$58)&$)¨ 4:2H73$)¨ f ! %*7 ¨8L 9\4:),+X0:%*)(?D4&%8> % ; +34B>Q+-5¦!3`+-LH%Y+-@5.)H! ¦Z2 4:7-4R+-2 4:7-4#%8734 ; E$4:),+/U\5*'¤¤¤¤¤¤¤)¦¤¤¤¤¤¨ 9I¦9B9¡ ! ¢ " £¡ ¤£¦% ¢-¢e¦ "¢3¢-¦¢ ¤£$9¤ ¦Z2 4:7-4 )¡ ¥ )©¢ ¨ 462 73$)¨ ; 7-5YS84B>+32H%*+#5.)H0¡4 ¦ 4%WS8467-%2¨84F5YS.4:7b+32 4Q0¡LH?D4>¢ 4,¢ 5.E$>467Z@)H4¦¥,LH%*E$@+/U!¦ 4[0:%8)¡¨.4¡+R%\!GE$ ¨82,+3E$UQ?D4:+G+-4:7R5.) 42H%WS.4#!3LH0P2%M7-4:S.4:7P!G46?A 97 )\>4 ; 4:)D>@)¨ 5.) . %*)H> N'_7-589 ¢ ) ¨¢ !3LH0P2+32H4:7-4M4XL"!G+[0:58)H!G+-%8),+-!+32D%Y+¨¤¨ ©¨ ©¨ 1 1¢ A 1 1 ¢ ) ¨¢ 58)HE@UQ5.)(+-2 4[>@9\46)H!G$58)%8)H>C+-2 4#'_L )H0¡+3$58) +32H%*+ ¨85YS84673)D!+32H4 ¥,LH%.!G"!3U,9\9\4¡+-73U5*' 1 ¢ ¦ 2 4C?5*+3+35.9 E$$) 4C"![+32D%Y+58E">4:7M@)H4¦¥,LH%*E$@+/U E$ 5.4!-%Y+3"!%H46!F%¨7346S84:7P!34? ¢ )= ¢ Q ? L+ ¦Z@+32N?D%*E$E$![7-4 ; E$%.0¡46> ?U 0¡L ?46!¦Z2 $0P2N> 5,4B![) 58+19Q%Y+G+-4:7 ¢ ¦ 2 $!; 4:7-9¦@+-!bLH!b+35(0:58)H0:E@LH> 4[+32H%*+¦Z@+32V?58LH)H> !b+32H%*+a>4 ; 4:)D>$!#%*) §¦ 46 ¨.2,+58)HE@UC5.) %*)D>C+-2 4&'_L )H0¡+3$58)+32D%Y+ ¨85YS.4:7-)H! +32 4 ¥,LH%.!G"!GU9\9\4¡+-73UQ58'£1 ¢?4606%*LH!34 5*'¦58L 7¨% ; 7-$587-!39¦558+32 ) 4B!3!Z%.!3!3L 9 ; +-@5.)]5.) 1?HL+R`+b> 5,4B!Z0¡5YS.4:7 +32 4[9Q%8@) ; 5.@),+P!¢¨ 4:2H73$)¨ f !b+32 46587-4:9$! ¥,L @+34¦73469Q%*7 5W%8? E$4F?D4B0:%8LH!G4¦@+ ; 7-5YS$> 46!aS84:7-U!/+-735.)¨5.)&+32 4"¦X%WUR$)@¦Z2 "0P2 ¥.LD%8!3$!3U9¦9\4:+37-$09Q% ;H; @)¨.!5.) '*)Q06%*)[>"!/+-5873+7-46!G+37-$0¡+3$58)H!4:) ),¢ + ; 7-5YS$>4B!%[9MLH0P2C!/+-735.)¨84677-46!G+37-$0¡+3$58)\+32D%*)Q"!¨.@S.4:)>"!/+P%*)H0:46!¦Z2>¢ 4©¢>$734B0+-E@UM?,UM+32H4R>4#H)H`+-@5.)5.7$)H>4:4B>¦Z2 "0P2¦"!+-73LH4Z@)¨.4:) 467-%8E+32D%*)!¦Z2H%*+"!b+-73LH4M5.)¨+32H4M7-46%8E^E$$) 45.7a5.) %*),+-587&!G4:+-!:¢ 587#$)H!/+P%*)H0:4@+[@9 ; E$@4B!a+32H%*+&@', "![%]?D%*E$E@).'*) )%*)H>.1 D '*) V '*) $! ¥,LH%.!G"!3U,9\9\4¡+-73"0+32 46).1N$!%80¡+3LH%8E@E$UV? $E@ ; !-0P2 @+^\58) ¥¤ 58' , ¢ )A'%80+?U % !306%*E$458)H4¦06%*) )H587-9\%8E@ ^:4 1, +35 ¨84:+(% L ) @'_587-9 ?58L )H> 5.) +-2 4¨? $E@ ; !-0P2 @+^¨0¡5.)H!G+-%*),+ ¢ ¦ 2H46!34'%80¡+35.7Q58)¤O4:9\9Q% ¢ & ¥¢ QM?4:E$5§¦@¢%8!-!34:73+3$58)H!X0:%8)]?4F>4673$S84B>C'_7-589'_587$)H!/+P%*)H0:4'_5.79\4¡+-73"0 ! ; %.0¡46!:¢ b+-2 4:77-4/¨8LHE$%87O9\4¡+-73"0=! ; %80:46! _ 4#H)H`+-@5.) ¢ ¨ +346739Q!X58'O+32H4#4XL$!G+346)H0¡4&5*'4Z@) 4¡¥,LH%*E$`+-@4B!X$! ¨.@S.4:)]@) T ?b4:$)§ 5,!%5W HI ¢58$)H0:%87§¦0¡LH73S.46!=%8735.L )H>¦+-2H%Y+X%*7-4R) 5*+ +3551E$58)¨4,¢ ¨ ¢%[9\4:+37-$0a! ; %.0¡4R58'+32 4a'_587-9©¨ '

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

Saved successfully!

Ooh no, something went wrong!