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A point p in a Riemannian submanifold is umbilical if, at p, the (vector-valued) Second fundamental form is some normal vector tensor the induced metric (First fundamental form). Equivalently, for all vectors U , V at p , II( U , V ) = g p ( U , V ) ν {\displaystyle \nu } , where ν {\displaystyle \nu } is the mean curvature vector at p .
The conjecture claims that any convex, closed and sufficiently smooth surface in three dimensional Euclidean space needs to admit at least two umbilic points.In the sense of the conjecture, the spheroid with only two umbilic points and the sphere, all points of which are umbilic, are examples of surfaces with minimal and maximal numbers of the umbilicus.
The shape also has a single external face. A cross section of the surface forms a deltoid. The umbilic torus occurs in the mathematical subject of singularity theory, in particular in the classification of umbilical points which are determined by real cubic forms + + +. The equivalence classes of such cubics form a three-dimensional real ...
Away from umbilical points, these two points of the focal surface are distinct; at umbilical points the two sheets come together. When the surface has a ridge the focal surface has a cuspidal edge, three such edges pass through an elliptical umbilic and only one through a hyperbolic umbilic. [3] At points where the Gaussian curvature is zero ...
The set of ridge points form curves on the surface called ridges. The ridges of a given surface fall into two families, typically designated red and blue, depending on which of the two principal curvatures has an extremum. At umbilical points the colour of a ridge will change from red to blue. There are two main cases: one has three ridge lines ...
Having two eyes allows the brain to determine the depth and distance of an object, called stereovision, and gives the sense of three-dimensionality to the vision. Both eyes must point accurately enough that the object of regard falls on corresponding points of the two retinas to stimulate stereovision; otherwise, double vision might occur.
At delivery, the baby's umbilical cord was triple wrapped around its neck; the girl was lucky to be alive. Evelyn's doctor told her that, in light of her history, it was not safe for her to get ...
Schematic representation of the theoretical (T) and the empirical (E) horopter. In vision science, the horopter was originally defined in geometric terms as the locus of points in space that make the same angle at each eye with the fixation point, although more recently in studies of binocular vision it is taken to be the locus of points in space that have the same disparity as fixation.