There are a few ways one can “hide” the edge linework.
STYLES : check the Style menu make sure the edge style is turned on.
HIDE : Entities in SketchUp can also be selected and hid by using the hide feature. You can see hidden edgework by going to View > Hidden Geometry. This will show you all the hidden and softened edge work. You will want to select the edges you want to show and select Edit > Unhide
Soften/Smooth Edges : To get the one surface look from a combination of mulitple surfaces, users often use the Soften Edges feature. This will visually remove linework from connected surefaces. You can reverse the look of this by selecting the smoothed surface and activating the Soften/Smooth dialog (Window > Soften Edges). By shifting the dialog slider to the left, it will remove the soften/smooth characteristics of the surface.
Under the Style menu, you will be able to select Profile to show the profile silhouette of the curved surfaces
Hope this helps