Arise, walk in the land [earth] through its length and its width, for I give it to you." Genesis 13:17 

Abraham was told to walk through the length and breadth of the land. The word for land can also be translated earth. We see that Paul speaks of Abraham taking hold of this by faith.

For the promise that he would be the heir of the world was not to Abraham or to his seed through the law, but through the righteousness of faith. Romans 4:13

So Abraham took hold of the promise of God by faith and by that faith he walked throughout the length and breadth of the earth. Abraham also looked for a City whose builder and maker was God. That city is described in Revelation 21. The dimensions of the city are two wide and high to find on a globe. And this is the reason why Abraham was to walk its length and breadth. When that City comes down to Earth, inspiration tells us this interesting fact:

The glory of the Eternal Father is enshrouding His Son. The brightness of His presence fills the City of God, and flows out beyond the gates, flooding the whole earth with its radiance. {The Great Controversy, p. 665.1}

If the light of God can reach the whole earth from the city, then again we see that the earth does not have curvature.