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.

One Reply to “Geometric Interpretations for Surfaces Using Technology”

  1. Nice job putting all of this technical information together. Good work, Lynn.

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