umbilic point造句

• The three main type of umbilic points are elliptical umbilics, parabolic umbilics and hyperbolic umbilics.
• Umbilic points generally occur as isolated points in the elliptical region of the surface; that is, where the Gaussian curvature is positive.
• Here Blaschke's index is twice the usual definition for index of an umbilic point, and the global conjecture follows by the Poincar? Hopf index theorem.
• "A conjecture " : He is credited with the authorship of the Carath閛dory conjecture claiming that a closed convex surface admits at least two umbilic points.
• All the proofs mentioned above are based on Hamburger's reduction of the Carath閛dory conjecture to the following conjecture : "'the index of every isolated umbilic point is never greater than one " '.
• In 2012, Ghomi and Howard showed, using a M鯾ius transformation, that the global conjecture for surfaces of smoothness C 2 can be reformulated in terms of the number of umbilic points on graphs subject to certain asymptotics of the gradient.