§3. Weierstrass preintegrands. Weierstrass integrals, as we shall define them on our Reimannian manifold M_{n}, are generalizations of R-length on M_{n}. With Weierstrass, was the (x,y)-plane, so that no presentation theory was required. However, general differentiable manifolds presuppose a set of compatible presentations. It is accordingly necessary to begin with a presentation (ϕ,U) in

To this end there is associated with each presentation^{∞}, subject to the homogeneity condition,

(3.2) F(u,kr) = kF(u,r),

valid for each pair (u,r) in the domain of F

EP - 33 PB - Princeton University Press PY - 1976 SN - null SP - 16 T2 - Global Variational Analysis: Weierstrass Integrals on a Riemannian Manifold. (MN-16) UR - http://www.jstor.org/stable/j.ctt130hkgk.6 Y2 - 2021/09/26/ ER -