Metric Structures for Riemannian and Non-riemannian Spaces M ...

?W938 KeJYCdJY?[­X?W9#2V z CLFS9vmaJW2_FI?W9@JNT¨mbZ–HGF_A>A>?[9"2j;>RpA>RS]^JsCLRP­SJYK>?W9#2jRIk V { • R_K_ ¡ Ÿ o V z RIk03G9@?[;>J3?W9GTUJd˜O?[;>=¡ ¨ - NY?BT OPz`{ ¢ A„O3JlHGF_A>AŽ;>R7A>hGCE=\CLRP­SJLKe?W9#2_AYM¨z FI9GT^?W9GAf;>JYF_T^RIk»;>=GJ7RSKe?I2S?W9GFIVU?W9X­”FSK>?BFI9b;EADRIk+VwMkuKeRS]+FyV[RPO3JLKDmˆRShG9GTwRS9>?BCLCL?ƒo=GFI; V ?WA3FI9sF_AfHG=@JLKe?WCYFIV :»¥TU?W]^JL9GA>?WRS9GFSVG]wFI9@?[kuRSVBTO?[;>=xFVKeJYA>?WTUhaFIVWV[ZW3G9@?[;>Jckuh@9GT@FS]1JY9b;eFIV 2SKeRShGHŽMaO=GJLKeJy;>=@J=GJsKeJYA>?WTUhaFIVU3a9@?t;eJL9@JNA>A1CdR_9GTU?[;>?WRS9 {– =@?BAcO?WV[V!V©¨?W9\;>=GJQA>Ĥ JYCd?BFIVXCLF_AfJ¿RIkaF…Ĥ RSVWZb=GJYTUKeRS9 9VVV ¥CLRXCE=aFI?W9GARS9 9 Ma?{J { ;>=@RbAfJykuhG9GC`;e?[R_9GA7R_9j;>=GJ¥maR_h@9GTUJNT MGFI9aT;e=@JL9iRS9GJ\TUJ3G9GJYA µˆ‰Iµ 9:‡4 · º I 4 · Vo¤zU- ‰SJYK#R ¤ R ¤ a Ÿ o¤ a Ÿ z ¡9VkˆCLRSh@KEA>JSM”?t;Š2_?[­_JYArZSR_h¦‹hGAf;DRSKETU?[9aFIKeZCLRS=@R_]^RSVWR|2SZ…kuRSK µ86½ 4 HaR_V[ZX=@JNTUKeF 9 MPm@hU;¤z _ ¤?BAFSK>?WV[Z¨CdVWR_A>JYTŽM¥CdR_=@RS]^RSVWR|2_Z z ?BAD9@RS;†FyAfJYHGFIKEFImGV[JA>HGFSCLJ {5 =@?WAVVVVVVV¤Q¢¡ ¢ !#© '(¡¤£Š© ¥¦¥¨§0! (0£(©K©¨©Š§#¥§£ ¢ ¢®>®f® { ®;\]wF”Zp=GFSH@Ĥ JL9–;>=GFI;\;>=GJ©oqCdR_9b;>KeRSVWV[JNT z CdRS9b;eKeF_C`;>?Wm@?WV[?[;‹ZpRSk3maFIVWVWA?W9 V%ouR_KFcCLRS9b;>KeRSVWVWJYTCLRS9b;>KEFSCd;>?Wm@?[VW?[;‹Z1RSkŽmGFIVWVBA¿?W9;e=@Jh@9@?W­SJLKEAeFIVaCLRP­SJYK>?W9#2 9 - .FSA¿O¿JYV[VJd˜@FS]1HGV[J_Mˆ?[k¿O3J^A‹;EFIK>;…O?[;>=¨FsCdR_]^HGFSCd;F_AfH@=GJLKe?WCYFIV8A>HGF_CdJV^M»;>=@JY9 O3J^TURs=GF”­_J3G9G?t;eJ^CLRP­SJYK>?W9#2_A . V IE‰Pµ 4L‡ xR6µ¢x ;>R . V { o =@JJY9GCdJ1RIk¿A>hGCE= .FSA…?W9©;>=GJJpbh@?W­PFIVWJL9b;r;>R;>=@J ‡4 ¸U6q· º Š w µ;6½ 4 µ 4 Ȩ¸ RIk ¡ Ÿ oR Š Ȩ¸ º t4 HaFSC‰X?[9"2\?[9GJpbhGFIVW?[;>?WJYAD?W9w;>=GJYA>JcouO=@?BCE=wkuR_V[VWRPOyMIkuR_KlJd˜@FI]^H@VWJSM. V(RSKRSk .O3JA>=GFSV[VŽCLRS]^Jyh@HgO?t;e=©F=@RbAfJRIkV {­SJYKeAeFIVDCLRP­SJLKe?W9#2 9 - .?BAyh@9GT@JLKcCLRS9b;>KeRSV{w =@JL9¨;e=@JFImˆRP­SJwFIVWVWRPO¦AFimˆRShG9GTRIkD;e=@JchG9@?¥. V ?W9©;eJLKe]^ARSk†­SR_V .RS9©;>=@JK3Jd;>;>?59Xh@]cmˆJLKEA7RSk{ ®:9pHGFSKf;e?WCLh@VBFIKNM ‰Iµ 4 I Š µ¨½ B º ¸­PFIKe?WFS9b;eA5FIKeJ¿]?WH@V[?BCLFI;>?W­SJQh@9GT@JLKlCdRP­_JLKe?[9"2_AYM ‰Iµ 47‡4 I Š Àˆ½º ‡4 ¸ Š De‰ º µˆ·Š Id½ 4L‡ 6BȨ½=@JNAfJ