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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 .
Finally they are geodesic ellipses and hyperbolas defined using two adjacent umbilical points (Hilbert & Cohn-Vossen 1952, p. 188). For example, the lines of constant β in Fig. 17 can be generated with the familiar string construction for ellipses with the ends of the string pinned to the two umbilical points.
The curvature lines make up the major and minor axes of the ellipse. In particular, the indicatrix of an umbilical point is a circle. For hyperbolic points, where the Gaussian curvature is negative, the intersection will form a hyperbola. Two different hyperbolas will be formed on either side of the tangent plane.
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 ...
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 projective space and the subset of parabolic forms define a surface – the umbilic torus.
The vertical lines are the mid-clavicular lines taken from the mid-point of each clavicle. The upper horizontal line is the subcostal line taken from the inferior parts of the lowest costal cartilages. The lower horizontal line is the extoturbular line connecting the tubercles of the pelvis. [3] [4]
"The center-hole was placed approximately 9 inches from the center of the basket, causing the arc of the 3-point line to be approximately 9 inches short at the apex of the arc," the statement reads.
McBurney's point is named after American surgeon Charles McBurney (1845–1913). [1] [6] McBurney himself did not locate his point in a precise way in his original article.The seat of greatest pain, determined by the pressure of one finger, has been very exactly between an inch and a half and two inches from the anterior spinous process of the ilium on a straight line drawn from that process ...