DifferentH Geometry and Gassman ni ns :Dg 6-

Recall fm Monday thttayut rats to QE an ) aeftefm QD whe D B Shen . symahrr & tht tight

Helms to IIQ ) E Va IR"

look like Q [0ps-BAT] whe AEOK) & B B kxh . h)

.

lihenie, tarot nets to THE burn look like Q [ is"Y ] fr B a kxh Y mtix

.

Thy: Tf p , } a point in a Riemannian) moitld M & expp : TPM → M B the expmhl hp,then

, all geodes is in Mthh p

are of the fm exppltu) for TETPM .

In pkk,gobsrstbh the identity in 04 are of the from exp ltd ) = et?

In th,

she left - troyklm this the idntty to yother port QEOH ) B a geometry . present way , geodesy thh QEOH are

of the fm Qeta

So now if we went geodesy in Her or Ga Rn,wrist restrict the appsprite do is fd :

Geodesistfh HQHKR "are f the fm HQ) et

%"¥& gwdesistyh Hal earn are f the fm Ita ) et

↳%?