It appears curved to us because we mathematically transformed the reference frame.
If you are allowed to transform your geometric space to say "no straight lines" then there are no straight lines in math either. Because you could perform a transform on the straight line into a curved geometry.
“I want to emphasize that light comes in this form-particles. It is very important to know that light behaves like particles, especially for those of you who have gone to school, where you were probably told something about light behaving like waves. I’m telling you the way it does behave- like particles.”
Richard Feynman, “QED The Strange Theory of Light and Matter.” Introduction, Page 15.