3D graphics are sometimes tricky.
I do some of my illustrations (when it does not involve a whole sphere or no things that overlap in a tricky manner, which TikZ/pgfplots, which has some 3D capabilities (just not z-tracing), see for example slide #3 (note #3 has a few images changing so slide #3 is only on page 12). The advantage is, this is well-programmable (Since you program the graphics in TeX) - but since it is TeX it is also to some extend limited.
The graphics you show – I am unsure how that was created, the lower (manifold) part especially – the tangent space might be a TikZ overlay actually.
I hope this gives a few starting points, I am not sure how the usual Manopt (Matlab) plotting facilities are.