4,052 research outputs found
Surfaces given with the Monge patch in E^4
A depth surface of E^3 is a range image observed from a single view can be
represented by a digital graph (Monge patch) surface . That is, a depth or
range value at a point (u,v) is given by a single valued function z=f(u,v). In
the present study we consider the surfaces in Euclidean 4-space E^4 given with
a Monge patch z=f(u,v),w=g(u,v). We investigated the curvature properties of
these surfaces. We also give some special examples of these surfaces which are
first defined by Yu. Aminov. Finally, we proved that every Aminov surface is a
non-trivial Chen surface.Comment: 1
Cyclic and ruled Lagrangian surfaces in complex Euclidean space
We study those Lagrangian surfaces in complex Euclidean space which are
foliated by circles or by straight lines. The former, which we call cyclic,
come in three types, each one being described by means of, respectively, a
planar curve, a Legendrian curve of the 3-sphere or a Legendrian curve of the
anti de Sitter 3-space. We also describe ruled Lagrangian surfaces. Finally we
characterize those cyclic and ruled Lagrangian surfaces which are solutions to
the self-similar equation of the Mean Curvature Flow. Finally, we give a
partial result in the case of Hamiltonian stationary cyclic surfaces
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