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.

7 l4s [!s {!|)~ R ¦ ~¨~|` P t d9`¤} s i s"P!s.rtz |)9 s ~-. ` s2tfP!sr ¦ ~ V=[!s ` rs _ j ~ ss ¢ t d9`¤} s ljP-R.sV=[!s ~ Vt d!| z |$9 s { P ` r _ Y „ Y 3 Y „ Y ¤ ¦ § ` P m j *X…Yl s O ¦ twz ~ V=[!s ` r |i'| P twz~|H‹C § ' E 0[gf)l` n( n I V } ) } %¡( V I2}. ) N aI*':n( g)S` I N V ' aI2} i . Z \ V } V \ V 0 V } iB$C)(} V .' Z %\y%.+% / }5`)a¥) ';' { . Z I2} V .' V . I( ) . I' V ) ( I aI2} i . Z \ V } V \ V 0 V } ioV } . Z I V (VI' / I ` . V7n I Z %\y%.+% /p} ` a) ';' I:' q(¡# # [ C ¤ P { s.s {+ V[ s z |b V `Cb V ` V=[!s ¦ P |)} sr ~ tz R `¤} s.r NxP_9-P | Vs i s `@{ s ~| RhV=[ t¡V {|)}@|){ s ~ |`8b V[ s ~ ¦ r b tCR.s |)~ tCPz |eb V tf[ | R;[ -¦ P t d z)s V `#| PVsr ~ s"RV t | V[ `C¦ V d s | P i P ` P _o| P |¥_+|)9.| P i t `C¦ z {t ¤ P^V[ |"~ Rt ~ s [ ` t s } sr z | s ` P ` P s ~|"{ s `Cb PNV¨s.r ~ sSR:V |` P tf[ | R;[At `C¦ z { Jsr _o| V ¦ ~ V ` ~ [ ` rVs"P | VLt | V=[ | P | V ~ [ `C_h` V ` §k Rz"t ~¨~ |[ ¦ ~ 3 s{¡Qu¦ ~ V¨s { V ` V[!s _h` r¨s i s"P!s.rtz ~| V ¦ t¡V |¥` P tf[!s.r¨s#rt8P m j *l A 3 {|_ * tVAV[ |"~Ad r | P i ~ t8P s - V¨r¨t^R ` P ~ V¨tCPV { s.\s2P {| P i\` P rt8P m j ~ s.s ¢ ¢ P | Pd5¦l ¦ ` ~ sV[ t8V ¥ 3 r¨tCP m j *l ¥ 3 {|¥_ * M{ sX9-P s ~ k ~ V { s i j lf`Cb V[ sj¡tCR Ǹd!| t8P _ t @ * m3¥J¤£ t ~ t d£`¤} s t8P { !r `¤} sV[!s b` z$z ` t | P i d9`C¦ P {¢Y Y 7 £ ~ k ~ V { s i j l`¢ z `Ǹ t8V V[!s y tr=P ` V c y twr¨t8V[!s `@{5` r=k _ sV¨r | R ~` P ¢ Vr ¦ R:V ¦ rs unr¨sV=[!s.r¨s+rst ~` P t d zk i s"P!s.rtz R ` P {| V |¥` P ~` P ~ ¦ R;[ _ sV¨r | R ~ tf[ | R;[~`C¦ z { s"P ~ ¦ rsV[!s z ` ts.r t ~ k _ V ` V | R d£Ǹ¦ P {A` PAV[!s y y cv}C` z ¦5_ s ~`Cb V[ s c~d tz)z ~t| P ~ ¦ R;[ ¢ 4 m d kWR ` P ~ V ¢ i r `C¦ tCRV | P ih` P ¢ 4 m4 ¢ ¤ PT twr V | R ¦ z"tr tsttCPV ~ ¦ R;[ d9`C¦ P {!~ b` rP ¨ ¢¡¤£¦¥¨§¦©£¦¥©£¥¡¥¥§¡¤ !§"#¤ §$¤%¦&'z)s2P i V[ftCR"R ` r {| P i V ` V[!s b` z$z ` t | P i N | PV ` Vut `¢{`C_ t | P ~ u_z `§` d t ~ s { ` P t8P { [ t }@| P i _o| P |¥_ twz z$s"P i V=[ | P ~`C_ s _¦ zV | !z)s `8b V=[!syRz"t ~¨~M`Cb t `C¦ z { [ t } sqt Ǹ¦ z { [Jt } s t8Vz$st ~ V ` P s ~ sz b cB$C)(\( 4 § ' Y ' ",*,( ! (#" ' A,£¦ 6( C j al < ¦ r€r¨st ~` P | P i Rt8P d s! r `S3 ?gl < PV[!s ` V[!srz[Jt8P {+ t s ~ [ tz)z@z)t8Vs.r ~ s.s b r `C_ t {| E srs"PV tCP i z)sV[ t8V0P s R.tCPTtwzt2tFk ~ 9-P { t ~ [ ` r VR ¦ r } sytf[ | R;[ |)~ P ` P c [ Ǹ_h` z `CiCǸ¦ ~ V ` 9 s.r `f| P *`{ b` r*tf[ | R;[4V[!s |¥_ !z | s { R ` P ~ Vt8PV { s.\s2P {!~f` P zk ` P 3F{|_ * 2 r `Cd t d z¥kt8PV[ |)~ R `C¦ z { tz ~ `hd s€tCR;[ | s } s { t | V[ft+r¨sX9-P!s _ s2PV `8b V[!s€twr iN¦5_ s2PVnt d9`¤} s ` P V[ s _ t ~~U`Cb V=[!s _o| P |_ tz e m j * …Yl i s"P!s.rtz |)9.| P i j gl%7 m ¨ }C` z * Wj 7 l 0 - V¨s2P { V=[!s z Ǹiw| R `8b V=[!s s - s.r;R |"~ st d£`¤} sUV ` V[!s ¢ tNR Ǹd!| tCP _ t! | P iA`8b V[ s;ns |)~ s2P d s.r i _ t8P |eb` z { 4 mx¡V ` J ¢ t | V[ t[ Ǹ_&` V ` k } sr ~|¥` P `8b~ k ~ V { s ijR `C_ twrs ¢ y ¦ | P! r `S3 ? l 0¥ l yz ! (#$" y ` P ~|"{ s.r ¢ j4 m t | V[ | V ~ R.t8P ` P | R.twzR ` PV¨tNR:V ~ Vr ¦ RV ¦ r¨s tCP {4 m R Ǹ_ t¡V |d z)st | V[WV=[ |)~jr¨st ~ ` P t d z$s l y y c~_ sV¨r | R ~ | P } tr | tCPNV ¦ P { s.r tyR ` R Ǹ_ JtCR:V*P | z) ` Vs"PNV |)~`C_ sV¨rk

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

Saved successfully!

Ooh no, something went wrong!