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.

; ; @)¨Q2D%8! +35(?D4[9\5> H46> W 58) 4[E$5525! '_587 ¨.735.L ; 2 589\589\5.7 ; 2H$!39Q!X@)H!G+34B%8> c9Q%5.7 7-46%8E ] SY%*E$L 46>C9\% ; ; $)¨.! 58)H4aE$5525!'_5.7 2H589\589\587 ; 2 "!39\! $).+-51+-2 4#734B%*E),LH9H]%8)!W¡ ¢ V4B!/+P%*? E$$!32 4B>Q>¡ 4:7-4:),+-$%8? @E$@+/U\%8E@9\5,!/+=46S84673U X 2 46734X'_5.7; !-0P2 @+^&9Q% ; ; $)¨,!Z?D4:+ X 464:) ¢R46$!34:)?4:7 ¨-¨.735.L ; ! +355}c¤K2H%*+b%*?58L+b58+32 467R4HL %89 ; E@4B! ¢ ©Z>5Q) 5*+ 5,)H5 X 5*'%8),U ! ; %80¡4B! X 2 4:7-4&+32H4:7-44¢R46$!34:)?4:7 ¨ ¨87-58L ; !D_ W ?HL+'©R>5])H5*+ 5) 5 X %() "0¡4M+32 46587-4:9c ] b 4:4\%*E"!35C+32H4%*)D>¨ 4 + ¤ + %¦@) T _ %WS b 4:9GW ¥¤¥§¦ W %8)H>]+32 4F> $!-0¡LH!-!3@5.)]$) T b 469GW £ ¤©¨$c _#¦ 2 4 ; 7-460:46>$)¨[>"!30:LH!3!3$58)¦5*'>¡ 4:7-4:),+-$%8? @E$@+/UM%*E$9\5.!G+4:S84673U X 2 46734 ; 7-5YS$>4B!4 4a!34:4R) 5 X +-2H%Y+ +32 46734b%8734Z7-4:9Q%87 5Y%*?HE@4Z7- ¨.$> `+/U¦734B!GLHÈ +P!+351?D4b'_58L )H> c ¦ 2H4:7-4R$!¨846) 4:7P%*E$@+/U>c%Y+X+-2H%Y+RE$4:S.4:E5*') +-2 4 ) 4HL+V!G4B0+3$58)D! X 4A!32H%*E$E[0¡5.)H!G">467(5*+-2 4:7V%.! ; 460¡+-!]5*'M%8)H%*E$U!G"!(%8)H>©' 46%8!3L 7-4b+-2 4:5.73U X $E$E?D4[0¡7-LH0:$%8E W %.! @+Z$!%Y+ZE$46%.!/+Z%¦E@@+G+-E@4&4:LD0¡E$$>4B%*)!/+-73LD0+3LH734ac¦ 2 46587-4:9 c) 3 c )>c ¨ 55>¨?4:2H%WS$587a+/U ; $06%*E$E@Ü > 5,4B!#) 5*+[50:0:L 7a$) %(L )H`'_5.739$)WFX $E$E ; E"%WUC%\E$%87 ¨.4a7-58E$4>cE$506%Y+-@5.)H!¨¨846589\4¡+-73U\>4B!G4673S.46!9\5.734#%Y+G+-4:),+3$58)(@)(+32 "! X %WU W '_5.7=+-2 4#!G+37-LH0]¢R46$!34:)?4:7b +346@)!W ¥ _ W ? L+ E@4B!3! %Y+3+34:),+-@5.)Q2H%8! ?D464:) ; %*">\+35¨84:5.9\4¡+37-U ] ? L+Z!G464 T ¨ 735§W£ ¤ Y_gcT2 46734#58L¨.2,+ +-5\?D4[9\587-4#+35Q!-%WUC%*?58L+ ¨846589\4¡+-73UC%8)H>%*)H%8E@U!3$! 5.) 0:4:73+-%*$)¦&§& &¨ 9I¦9B9¡ ! ¢ " £¡ ¤£¦% ¢-¢e¦ "¢3¢-¦¢ ¤£$9¤ ?4:7P! W ? L+%*)H!3L T"!#!3589\4:+32 $)¨E@ 584\>3 467346).+-$%8? $E@@+/Ü %*E$9\5.!G+#46S84:7-U X 2 4:7-41?HL+ X 2 4:7-4F+-2 4 ¨84:5.9G]$!&) 58+ ; 7-%.0+-$06%*E$E@UV46LH0¡E$$> 46%*) 587[% 7-4:E"%Y+3$S84¦5*' +32 4 ¢b4:"!G46),?4:7 ¨ ¨87-58L ;h] 5.74¡+-73U¤ @_gc H5871%! ; %80:4QE@ 584¦+-2 4 b $4:7 ; $)H!%506%*7]%*)eW£5*+-2 4:7 %873)H5*+ ¨87-58L ; ! W %.![$) T4¡+R>46!-0¡7-$?D4B>C$) b 4B0+-@5.) c 3 58)H4#06%*)(2H5 ; 4b'_5.7 ?4¡+3+3467Z?D462H%WS@5.7=+-2H%*) %*),+35.7;5 X D%65.46! ] ? L+\) 58+\!3LH0P2 ¨.55>N?D462H%WS@5.7M%8!1'_587\46LH0¡E$$> 46%*) ! ; %.0¡4B!!34¡+-!\%8)H>N!3)¡ §§¦¢ ¡> ¤ ¥¦ ¨,§-@@ +¥BÄ §DLH! X `+-21%R) "0¡4=5 ; ; 5873+3L )H`+/Ua+35aS,$4 X 46S84:7-U,+32 $)¨Z$)%*73+&© © X @+32M>4:4 ; !GLD! ; "0¡$58)@c) 58+32 $)¨1E$ 584Z+-2H%Y+X@)%*73+ © © W %*)H>C@)H> 4:46>C) 5*+-2 @)¨1E$ 5.4 ¦ 2 4:5.73469 c ) 3 c) X 587 5!¨846589\4¡+-73UQ9\5.734&!G46)H!3`+-@S.4b+-2H%*)%*73+ © ©gc ' 5.!G+X5*' @+ X @E$EK?4[%*?58L+R! ; %80:46! X `+-2%WU]'_5.7[%*E$E ; 5.@),+-! W 58)HE@Ü %*+&9\5,!/+ ; 5.@),+P!c ¦ 2 4M">4B%]58' , ¢¡ W@X `+-2AL )H`'_5.739X?4:2H%WS$587['_5.7 ; 4:7P0¡46),+15*'Z+-2 4 ; 58$),+-! W LH) `'_5.739\E$U %*+¦%8E@E !306%*E$46!F%8)H>¨855>+3LH734[58' 9Q% ; ; @)¨,! W 734B0¡52¨.) ^:$)¨X 2H4:)%Q! ; %.0¡4&2H%.!Z% ; ; 7-5 L@9Q%*+34:E$U ¢R46$!34:)?4:7 ¨W 4¡+-0>c + )H%*E$U!G"!Z5.)]+-2 4 ¢b4:"!G46),?4:7 ¨¨87-58L ; %8)H> `+P!b!3@9\$E$%873@+3$46!X+-5Q4:L!]?4:2H%WS$587?4:4:)(91LH0P2 !/+-LH>$46> ] !G464 T 5.E b +34W ©¡¢ W T 58E¡ b +34W W T ¡ 4:7W W0¡E$">46%8)(%*)H%8E@U!3$!=2H%8!$!a%WSW%8@E"%*?HE@410:L 7-7346).+-E@Uac b @467 ; @)H! 5^06%*7 ; 4:+-!b58L¨.2.+Z+-5(?4:2H%WS.4'_7P%80+P%*E^!G4:+-!Z+-2H%*)!3) 5 X D%25846!&%8)H> %*),+35.7F!G4:+-![@' )H5*+1%8! X 4:E$E=%.!&4:LH0:E@">46%8) ! ; %.0¡4B!?4¡+G+-4:7[+-2H%*)%*)D> ¢b4:"!G46),?4:7 ¨¨87-58L ; !.c ¦ 2 46UV2H%WS84¦E$5*+-!#58' 7-460+-1%*? E$4¦0:L 7-S846! W '_587&$)H!G+-%*)D0¡4 W%*E@+32H58L¨.2V) 5*+&!G5C9Q%8),U%8!a4:LD0¡E$$>4B%*)¨! ; %80:41%*)D>+32 4 ¢R46$!34:)?4:7 ¨¨87-58L ; c b $4:7]$)H! 5,¨,%8! 584:+-!X%*)H>('_7P%80+P%*E+37-4:4B!X2H%WS84a'_4 X 4:7R!G+3$E$E? L+b%*E"!35M46) 58L¨.2(+-5Q0¡58)H) 460¡+;; %*$7[5*' ; 5.@),+-!.c.# ¨ LHU f ![? $7P>2 58LD!G4 % T _ %WS">W £ IA"!F%8) 5*+-2 4:7[4XL%89 ; E@4¦+-5%*)Ub 4:4 T %*7-E@5 X WR%8)H> T %87 %.!3! WX'_587C%8) @),+346734B!/+-@)¨ ; 4:7P! ; 4B0+3$S84V5.)0¡5.)H!3$>467.c5.) '_7-%.0+-%8E!G4:+-!.c%*)D%*E$U!3"!

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

Saved successfully!

Ooh no, something went wrong!