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.

2H%*+2H% ; ; 4:)D!`' X 4 X %*),+1C+35&?D4 ¤K ; !30P2H`+I^ ¢ ¦ 2 "!0¡5.737-46! ; 5.)H> ! +35¤¢ l=) W4L+ ¦ 2H4:587-4:9 c c \>546!X) 58+R% ; ; E$UC+-5¦+32H%*+b0:%8!34>c© ) '%80¡+R`+b06%*) )H5*+ D?5.L 7-@467R!G4673$46!.c+="!) 58++37-L 4Z+-2H%Y+ ¨ w ¨¡w©/4 §¨ ¨#4HL ;`] 3 ¨¨ ©$_ ¦¥ ¥ @9 ; E$$46!=+32H%*+ 1C"! ¤O ; !30P2 @+^ X 2 4:)¢ l=) W ] ©$_4XL"!G+-!=%8E@9\5,!/+=46S84673U X 2 46734R%8)H>Q>4#D) 46! %&'_L )H0¡+3$58)C$) £ ¦¢324 '_587 %*E$E§7 ¥ ¥ W1'%80+Z+-2H%Y+ 1 ( , ¢¡ ] 'f_gc%*)D>($)%Y+^6)!W†c2 4[0¡5.)H0¡E$LH!3@5.)(58'O+32H$!Z!G+35.73UQ"! +32H%*+Z) 5*+-2 @)¨¦E$ 584[>3 467346).+-$%8? $E@@+/U(%*E$9\5.!G+¦c c) c4 4C!G2H58L E">A+32 46734:'_587-4¦)H5*+F4HL ; 460¡+1%*)U 7- ¨.$> `+/Ü E$ 584 ¦ 2 4:5.73469 c ) 3 c ); %80:4 X 2 $0P20:%8)]?4[7-46%*E$ ^:46> %8!Z%\!3) 5 X D%2584>c58)%*)UC9\4:+37-$0[!2H%*+\%8?D5.L+¦58+32 467\9¦4:+37-$0 ! ; %80:46! ¢ ©/!M+32 "!-5,$)H> 5*'b7- ¨8">`+/U ; 460:L E@"%*7¦+-54; %80:46! X 2 5,!G4¨.4:5.9¦4:+37-U "!1!3589\4:2H5 X % ;H; 735 L$9Q%Y+346E@UA4:LH0:E@">4B%*)£¢ ¦ 2 4CE$5YS846E@U!¡ ¢ £¢¥¤§¦¢¡¡+£©¨ ¦ £¢¥¤ ¢ ¦¢¤££ ¢ !©"¢£¢#£$% £ &§& © ' 1V"! ¤K ; !-0P2 @+^ W +32 46) w ¨¡w¥ ¥ ¦ ] c ) 3 c Qa_) ; %87G+-$0:L E"%*7 X 4¨2H%WS.4+35N2H%WS.4 ¨ V %.!¦ V ¥ $) 587P>467Q'_587 1 +-5 ?4©; !-0P2 @+^ W ? L+¦!¥,LH%8734] !3L 9\9Q%*? $E@@+/UV"![91LH0P2N!G+37-58)¨84:7#+-2H%*) +-2H%Y+9c)© +1"![46%.!GU¤KX 2,U ] c ) 3 c Q>_ 2H%.!X+35(?D4[+-73LH4>c © )V5.7-> 4:7X'_5871V+-5C?D4 ¤K ; !30P2H`+I^ X 4[2H%WS.4+35C!34:41 ] ©F_ W +P%65846)]$) +32 4F!34:)D!G4&5*'>"!/+-73$? L+-@5.)H! W !G2H58L E">(?4F?58L )D>46> c+35Q2D%WS84a+32H%*+4:+G+3$)¨ ¢"l )[$) ] c) 3 c & _ X 4[2H%WS84&+-2H%Y+ 1 ] ©F_Z$!Z7-4 ; 734B!G46).+-46> ?UC+-2 4) 5.L 7-@467b!34:7-@4B!1 ] ©$_vl] c ) 3 c _)(5.7-> 4:7'_5.7=+-2 "!+-5M?4b?58L )D>46>(`+Z!G2H58L E">QE$@4#@) £©@'=%*)D>V58) E$U`'w ¨ w¨E@50:%8E@E$U W %*)D>\+32 "! ; 4673$5>"0'_L )H0¡+3$58)AE@$46!a@) £¥ ¥ W ?UV!G+-%*)D> %*7P>734B!GLHÈ +P!b%*?58L +? L+Z+-2 "!X$!Z0:E@5,!G4a+35\?4:$)¨¦+37-L 4 W $) +32 4[!34:)H!34#+32H%*+ ¨ w ¨ w¥ ¥ $9 ; E$@4B! +32H%*+)H$0:4F'%80¡+ D @' 1 $!#%8!b@) ] c) 3 c & _ X `+-2 ¢ lg) W %8)H>V@' 1A$!#>3 467346).+-$%8? E$4+; 58$),+ W +32 46) ḦV %.! ¦ V ¥ c b 4641+-2 4)D7-!G+#0:587-58E$E$%873U]58) ; c ) %Y+&%]!3$)¨8E$45*' TX 2 4:7-4[2 58E"> !R'_587 ¢ ¤ 58E">4:7#0¡5.).+-@)L 5.LH!Z'_LH)H0+-@5.)H!b58'587P>4:7 ¥P) W %*)H>2H4:)H0:44:S.4:7-U58+32 $)¨QE$ 5.4F>3 467346).+-$%8? $E@@+/U(%*E$9\5.!G+R4:S.4:7-U X 2H4:7-4b'_5.7¥¤K ; !30P2H`+I^&'_L )H0£]+32H4:7-4[$!X)+32 4V46LH0¡E$$> 46%*) !3) 5 X D%65.46! ] '*) w 1 " © w ¢}_ W ¥ ¢ ¥ )>c + È +-2 58L¨.2+3$58)D!\58)!G+37-LH0¡+3L 7-4C"! ; E$46%.!3%8),+['_587\>$!-0¡LD!3!3@)¨E$%.0¡L )D%*7-U 5.L 7-@467M!34:7-@4B! W % ; ]4:LD0¡E$$>4B%*)7-5 L@9Q%Y+-4:E$U[+32H4a!-%*9\4Z?D462H%WS@5.7=0:%8)\?D4Z'_5.L )H>Q$) ¦ 2 46587-4:9 c c [%*)H> ¤O4:9\9Q%;X 4:7Q"!Q) 5}c ¦ 2 46734V"!C% S8467-!3$58) 5*' ¦ 2 4:5.73469 c) 3 c ) '_587Q+-2 4 ¢R46$!34:)?4:7 ¨%*)D!; !c § ) 4\2H%.!#+35V?4C%]E$@+G+3E$4C0:%8734:'_L E$) > 4#H) $)¨+-2 4Q0¡58)D0¡4 ; +F5*' > ¡ 4:7-4:)!]¨87-58LX 2 4:7-4X'_587 '_L )H0¡+3$58)H! 58)C+32 4¢R4:"!34:)?D467 ¨)¨87-58L ; W ? L+X`+ $!+3"%*?H@E$`+/UQ%8E@9\5.!G+=46S84:7-U4\!3%89¦4M%8!b'_587#4:LH0:E@">46%8) ! ; %80:4>c § )H41LH!346!b+37P%*)H!3E"%Y+3$58)D!R%*)H>A>$E$%"]?H%.!G"0:%8E@E$U(+-2; !32 58+-!58' %¨8$S84:)C'_L )H0+-@5.) W %*E$E !G)H% ; !32 5*+P!=E$@S$)¨¦58)Q+-2 4aLH) `++3$58)D!=+-5F+P%6584&!3)H%W %*)H>\+-2 4:)]58) 4#%8! 5!+32D%Y+ +32 4#E@$9\`+X4HL"!/+X%8! NV c ¦ 2 4a0:58)H0:4 ; + 5*'OE$$) 46%87?H%8E@E

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

Saved successfully!

Ooh no, something went wrong!