A geostationary satellite does not trace a path over the surface of the earth because that is what geostationary means - the satellite is stationary over a point on the Earth.

A geostationary orbit will keep the satellite in one area relative to the surface

Geostationary satellites are in an orbit that's 22,282 mi (35,786 km) above the surface of the Earth. For more on Geostationary satellite orbits, visit http://www.idirect.net/Company/Satellite-Basics/How-Satellite-Works.aspx

it carries wind into the earth.

they fly in air