MINIMAL OBJECT ON THREE DIMENSIONAL SURFACE
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. <br /> <br /> <br /> A bounded region on the surface in R^3 has an area....
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/26013 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | 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. <br />
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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. <br />
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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. <br />
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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. <br />
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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. <br />
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