Yanhua Yu

Structure and characterization of ruled surfaces in Euclidean 3-space

In this paper, using the elementary method we study ruled surfaces, the simplest foliated submanifolds, in Euclidean 3-space. We define structure functions of the ruled surfaces, the invariants of non-developable ruled surfaces and discuss geometric properties and kinematical characterizations of non-developable ruled surface in Euclidean 3-space.

A CHARACTERIZATION OF PARABOLA

In this paper, the parabola will be characterized as the plane curve whose curvature function and support function satisfy a condition, where we define the support function as the distance from origin to the tangent line.

Flat centroaffine surfaces with parallel second fundamental form in R4

By solving certain partial differential equations, we obtain some classification results for flat centroaffine surfaces in R^4, under the condition of parallel second fundamental form and vanishing Pick invariant. We also get some examples for flat centroaffine umbilical surface with parallel second fundamental form.