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

#n8)Zr n q\WZpZs*r3u :Q8 n#n8-@Au6 q pQr‚.(p0" tq1) a 82 …Pj @:p~)082+u qvs?pt>r nvn .(p+"t q;)u a e "($+r#"8#:Ur nvn "($+pZu p a e r#+s_)r n#n q\" a©¨ | l ¥ 8#"p9"($+r#"7"($?pAu(' { tp0.`'!. 82:-r aK82'!+s?pZs`:/r#.(q nOq;)uWqvu8r# rq1[r€.(p0" tq1) | 3p0?pZtr n j "($?q9uWu(' { tp0.`'!. .(rO/ap\q\ ©g?qV"p r#"8#:7.(p+"t{ rqvtu‚8#: { 8q1G"u q1 …Pj a!'d"_8#"($+pt%@Gqvu p§qV" n88 u n q p r .(p0" tq1) | ~ 4 n pHrt nOu(82.(pa ¨ . ar q16r#O[.(p+"t q;) u { r2)p l …©R a ~ ¥qV: l …©R a ~ qvu ¨¥A)B"#£;£j "%$?p0 a ¨ U ar j r3un p! #"%$+up8#:¢¡¤£¦¥¨§¦©£¦¥©£¥¡¥¥§¡¤ !§"#¤ §$¤%¦&'3r2.Jp n p0! 2"($ uB" t%'*)?"%'?t p | ¥ p pt("($?p n pHu u j @:p6r# rq1Mp. { $+ru q\WZp@:pr8ad"rq\b"($+p©u"($r-" 88 q1Z p?ptr n |U ¤ u v ] fR`^?b i!MfKhGia6bOaGi hiZ_g`iHgE_0a :"&@s8 n p! #"%$[uB" t%'*)+"('?tpZuGr2 tppu(82.(pZ8 { p0 uB'!au p0"u€)+8 ptq\* …Pj "($?p "%$?p0O rtp/8a q182'u nO p q '+r n | 4 82!>82pZtu p nO j q\: @:p¤rtp q p r )+8 ptq\* 82: … aOb8 { p uB'*a+u p0"u … @:Q8t U G jp0"($?pZt~@Gq\"($ n p! #"%$'uB" t%'*)?"%'?t pHu 8 @ 82 "($?p … @ @m$?q;)=$'rt p_)+8. { r-" q1a n p 8 "($+p"(8p)?"q\8+u … @¡ …£¢ :Q83tGr nvn TR¥¤ U G j "%$?p0r"($+ptp~8a q182'+u nOJp 6 qvuB"u>r l '!?qq '?p ~q1"ptup0! 2"($ u&"t('*)+"('?tpr82 … "($+r#"§t pHu&"t q;)?"u "%8 8 @8MpHr2)=$ … @ | l 8#"%$?ptT@P8ts?u jn"($+p n p0! 2"($[u&"t('*)+"('?tpZuP)+8. { t q9u pWr$ T+£ 8 pt§¦ | ~mƒ €"%$?p~82"($?pZts$r#+s j .(p+"t q;)u82 … rt pT!82" n8d)Zr nWl "($?pO :Q83t(. 82 nO'r{ t pHuB$+pZr-:98 pZt …'~4j a!'d" "($?pO )Zr# a-p"#H¨0"¡" Q¥( 704$(H£1 aO a |9M $?qvuj.(pZr#u9"($+r#"z:Q8tWpZr2)=$ b U …Pj "($+ptp p 6 qvuB"uWrrtp?pZq\ $GaK8t%$!88s S B Z… 82: b uB'g)=$`"%$+r-" a rm V ¦ a e rm V| ¥ 8-@ "r pP"($?p8uB' { t p. '!.tq q9r n rt( '!.(p0G"AuB$!8-@Au l u pZp p)+" q182 w|n a-p n8-@ ~4|r`"E !$K H !$#N-X* L * H L L E ajO iOfgs .Jp0" tq1)'u { r2)¦p l …©R a ~ q9uQr )?¡T ¥§£¦.4/¨'$.)?3¨£ q\:‚"($+p)+'+t pZuQf&8q1?q1! T"($?p { 8q1G"u l q | p |vj q\: a U asr ~¦|sq9u&"r#*)p`a-p+"&@:pp¤pHr2)=$ { rqvt~82: { 83q\G"u8p q '+r n u~"($?pJq\ ©*. '!. 8#: "%$?p=b/ach2 ¥ 8#"pz"($r-" j r)0)+83ts?q\! "%8‚"%$?qvu:sp ©*?q\" q182["%$?pWp'*) n q9spZr2 { n r#?p8qvuFr-R^!r#"($Z.(p+" tq;)Yu { r)¦p j a*'d"m"($?p { n r2?pX@GqV"%$6rJu p0 .(p0G"Gt p._8 pZs qvu B0.|{$?p¨©y>;u { $?pZt p 6 † qvu !8#"(r { r#"($c.(p+"t q;) u { r)¦p[@m$?pKp q '+q {?{ pZsc@GqV"%$c"($+pMq;)¤q1+sd'g)¦pZs aO "($+r#"r82: 0 † ] u j a!'d"6qV" 9$ r { r-"%${.(p+"t q;)u { r)¦p :Q8tr"($+p.(p+"tq1)p.(p+"t q;)paO m t%8 { 83u qV"q\8 w3|3+|p8spZum r-"%$U.(p+"t q;) u { r2)pZu>rsd.(q\"m"($?p :Q8 n#n8-@Gq1! §u q1. { n p‚)=$rtr2)?"ptq\WHr-"q\8 | ( $¢‚acf_0aG$-T+£R¦"¡"# ¡c$.)+¨£ l …©R a ~A0£W£¦¡ 0"v£¦