▁to ▁G rom ov ▁and ▁B user - S arn ak , ▁and ▁can ▁be ▁found ▁in ▁. ▁There ▁is ▁also ▁a ▁version ▁for ▁metrics ▁on ▁the ▁sphere , ▁taking ▁for ▁the ▁syst ole ▁the ▁length ▁of ▁the ▁smallest ▁closed ▁ge odes ic . ▁G rom ov ▁conject ured ▁a ▁lower ▁bound ▁of ▁ ▁in ▁ 1 9 8 0 : ▁the ▁best ▁result ▁so ▁far ▁is ▁the ▁lower ▁bound ▁of ▁ ▁obtained ▁by ▁Regin a ▁Rot man ▁in ▁ 2 0 0 6 . ▁ ▁Reading ▁guide ▁One ▁of ▁the ▁most ▁compreh ensive ▁intro duct ory ▁surve ys ▁of ▁the ▁subject , ▁chart ing ▁the ▁historical ▁development ▁from ▁before ▁G auss ▁to ▁modern ▁times , ▁is ▁by ▁. ▁Account s ▁of ▁the ▁classical ▁theory ▁are ▁given ▁in ▁, ▁ ▁and ▁; ▁the ▁more ▁modern ▁cop iously ▁illustrated ▁under grad uate ▁text books ▁by ▁, ▁ ▁and ▁ ▁might ▁be ▁found ▁more ▁accessible . ▁An ▁accessible ▁account ▁of ▁the ▁classical ▁theory ▁can ▁be ▁found ▁in ▁. ▁More ▁s oph istic ated ▁gradu ate - level ▁treat ments ▁using ▁the ▁Riemann ian ▁connection ▁on ▁a ▁surface ▁can ▁be ▁found ▁in ▁, ▁ ▁and ▁. ▁ ▁See ▁also ▁Z oll ▁surface ▁ ▁Notes ▁ ▁References ▁▁▁▁ ▁; ▁translated ▁from ▁the ▁Russian ▁by ▁K . ▁Vog t mann ▁and ▁A . ▁Wein stein . ▁▁▁ ▁; ▁translated ▁from ▁ 2 nd ▁edition ▁of ▁ ▁Le ç ons ▁sur ▁la ▁gé om étr ie ▁des ▁esp aces ▁de ▁Riemann ▁( 1 9 5 1 ) ▁by ▁James