Let
M be a two-dimensional Riemannian manifold with nowhere zero curvature and let
D1,
D2 be two smooth one-dimensional distributions on
M orthogonal to each other at any point. We present a method of seeing whether
M may be locally and isometrically immersed in R
3 so that
D1 and
D2 give principal distributions, and in the case where
M may be immersed in such a manner, we specify the values that may become principal curvatures at each point of
M. In addition, we study relations among the first fundamental form, the principal distributions and the principal curvature functions on each of a parallel curved surface and a surface with constant mean curvature in R
3.
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