论文标题
三个空间中代数表面的临界曲率
Critical Curvature of Algebraic Surfaces in Three-Space
论文作者
论文摘要
我们从代数几何学的角度研究了平滑代数表面$ x \ subset \ Mathbb r^3 $ o $ d $的曲率。更确切地说，我们考虑脐带曲率的脐带点和点。我们证明，复杂的临界曲率点的数量为$ d^3 $。对于一般的四边形，我们充分表征了真实和复杂的脐带和临界曲率点的数量。
We study the curvature of a smooth algebraic surface $X\subset \mathbb R^3$ of degree $d$ from the point of view of algebraic geometry. More precisely, we consider umbilical points and points of critical curvature. We prove that the number of complex critical curvature points is of order $d^3$. For general quadrics, we fully characterize the number of real and complex umbilics and critical curvature points.
