It is an HDR image on a curved surface, what do you expect? The HDR was probably created on a flat plane so it will be deformed on a curved surface.
John Hackney, Retired
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Look at the individual faces. See where the reflection breaks into a warp ?
Please provide the model in .f3d format. I am fairly confident I can pin-point the reason for this, but I would need to see the file!
Here as requested
The reason the curvature looks strange in those transition areas is that you are dealing with simple tangent surface transitions. For better surface transitions you need to use splines for these corner fillets with G2 curvature continuity.