I am using ArcGlobe.
I created contour lines using the contour tool, but some of them are not connected and are just fragments of lines, is there any tool that could connect these lines?
You said that you are using the ArcGlobe application of the ArcGIS Desktop product so I am assuming that you accessed the Geoprocessing Framework from there and used the Contour tool.
I think that you should use the editing tools of ArcMap (the main application of ArcGIS Desktop) to digitize lines that span the gaps in your contours.
You would need to set your snapping environment appropriately first. The About snapping page is where I would recommend starting if you are new to snapping in ArcMap.