ftware ▁development ▁events ▁Category : H ack ath ons ▁Category : Non - pro fit ▁organizations ▁based ▁in ▁Toronto <0x0A> </s> ▁In ▁mathematics , ▁the ▁principal ▁orbit ▁type ▁theorem ▁ ▁states ▁that ▁compact ▁Lie ▁group ▁acting ▁smooth ly ▁on ▁a ▁connected ▁differenti able ▁manifold ▁has ▁a ▁principal ▁orbit ▁type . ▁ ▁De fin itions ▁ ▁Suppose ▁G ▁is ▁a ▁compact ▁Lie ▁group ▁acting ▁smooth ly ▁on ▁a ▁connected ▁differenti able ▁manifold ▁M . ▁ ▁An ▁is ot ropy ▁group ▁is ▁the ▁subgroup ▁of ▁G ▁fixing ▁some ▁point ▁of ▁M . ▁ ▁An ▁is ot ropy ▁type ▁is ▁a ▁conjug acy ▁class ▁of ▁is ot ropy ▁groups . ▁▁ ▁The ▁principal ▁orbit ▁type ▁theorem ▁states ▁that ▁there ▁is ▁a ▁unique ▁is ot ropy ▁type ▁such ▁that ▁the ▁set ▁of ▁points ▁of ▁M ▁with ▁is ot ropy ▁groups ▁in ▁this ▁is ot ropy ▁type ▁is ▁open ▁and ▁dense . ▁The ▁principal ▁orbit ▁type ▁is ▁the ▁space ▁G / H , ▁where ▁H ▁is ▁a ▁subgroup ▁in ▁the ▁is ot ropy ▁type ▁above . ▁ ▁References ▁ ▁Category : L ie ▁groups ▁Category : Group ▁actions ▁( math emat ics ) <0x0A> </s> ▁Mark ▁Mi y oshi ▁is ▁a ▁Japanese - American ▁ta iko ▁mak er . ▁He ▁is ▁the ▁owner ▁and ▁principal ▁craft s man ▁at ▁Mi y oshi ▁Da iko , ▁based ▁in ▁M t . ▁Sh asta , ▁California . ▁ ▁Early ▁life ▁Mark ▁Mi y oshi ▁was ▁born ▁and ▁raised ▁in ▁Gree ley , ▁Colorado . ▁He ▁attended ▁the ▁University ▁of ▁Colorado