MINIMAL OBJECT ON THREE DIMENSIONAL SURFACE - ARYA SAPUTRA (NIM: 10114036), BAGUS
Curves and surfaces are mathematical objects in R^3. The shortest curve is one of the things to look for when there are two points located in different places. This shortest curve is called the minimal curve. A bounded region on the surface in R^3 has an area. The smallest area is one thing to look for. The surface that causes the area of a bounded region on the surface becomes the smallest is called minimal surface. The minimal curve and minimal surface properties in R^3 can already be determined. Based on this, we will determine minimal curve properties and minimal three dimensional surface in R^4. This final project re-modeled the curve and three dimensional surface in R^4. The three dimensional surface is constructed with a parametrization from R^3 to R^4. The arc length of a curve, the volume of a surface, the vector field, and the covariant derivative will be redefined in this final project. First fundamental form, second fundamental form, Gauss equation, and Weingarten map will also be reformulated. The method used in this research is literature study. The result of this final project is the geodesic equation on three dimensional surface in R^4, the relationship between minimal curve with the geodesic shortest curve, and minimal surface relation with minimal volume.