Of course! The term you might wanna start off googling is "curvature of manifolds". What's even neater than "3d thing curving in 4d space" is that these notions

Of course! The term you might wanna start off googling is "curvature of manifolds". What's even neater than "3d thing curving in 4d space" is that these notions can be made precise also without the "in [whatever] space" part (see "intrinsic curvature" and "Riemannian manifold").