"Classification of rational normal curve of constant curvature in hyperquadric"

Abstract: Rational normal curves is an interesting variety in geometry. In 1988, Professor Jensen etc gave a metric characterization of it. Equip CP^{n} with the Fubini-Study metric, they proved up to U(n+1) and automorphism of CP^{1}, every holomorphic CP^{1} of constant curvature in CP^{n} is a rational normal curve.Based on this result and singular value decomposition in linear algebra, we give an approach to classify rational normal curves of constant curvature and degree d in hyperquadric Q_{n-1} , up to real orthogonal group and automorphism of CP^{1}. As an application, we classify such curves when the degree d is less than or equal to 3. 

Host: Yanli Song