Geometric Interpretations for Surfaces Using Technology

By Lynn Sherman

Faculty Mentor: Professor Y. Jen Chiang

This presentation is based on Math 491- Differential Geometries taken in Spring 2021. We first define the coordinate patch of a surface and provide a few examples of surfaces. Then we construct the tangent space and normal vector of a given a surface. Afterwards, we compute first fundamental form, second fundamental form and Christoffel symbol of a surface. Then we define mean curvature and Gaussian curvature of a surface. We also will discuss geodesic and parallel vector field of a surface. In the mean time, we will utilize Mathematica technology to sketch the graphs of various surfaces.