http://swrc.ontoware.org/ontology#UnrefereedArticle
測地線・曲率テンソルとSageMath
ja
Riemannian Geometry
Differential Geometry
Geodesics
Cur vature Tensor
Computer Algebra System
伊藤 誠
The curvature tensor of 4-dimensional spacetime, which appears in general relativity, is difficult to understand because it is a complex tensor with four subscripts. Since it is impossible to visualize geodesics and curvatures in 4-dimensional spacetime, we visualized geodesics and calculate curvature tensors of 2-dimensional surfaces, which corresponds to a 2-dimensional Riemann plane in 3-dimensional Euclidean space in order to understand the meanings of geodesics and curvature tensors. For the visualization and the calculation, we used SageMath, which is a free computer algebra system software. We found that the visualization of these geodesics and the calculation of curvatures on a 2-dimensional surface in 3-dimensional Euclidean space is useful for understanding their meanings. The usefulness of SageMath is also clarified.
大阪産業大学経済論集
23
2
1-17
2022-03-31
大阪産業大学学会
1345－1448
AA11394639