2023-02-08T12:32:23Zhttps://osu.repo.nii.ac.jp/?action=repository_oaipmhoai:osu.repo.nii.ac.jp:000024582022-09-29T15:00:00Z0001900019:0052700019:00527:00530
測地線・曲率テンソルとSageMathUnderstanding Geodesics and Curvature Tensor using SageMathjpnRiemannian GeometryDifferential GeometryGeodesicsCur vature TensorComputer Algebra Systemhttp://id.nii.ac.jp/1338/00002403/Departmental Bulletin Paper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 = OSAKA SANGYO UNIVERSITY JOURNAL OF ECONOMICS2321172022-03-31大阪産業大学学会AA11394639https://osu.repo.nii.ac.jp/?action=repository_action_common_download&item_id=2458&item_no=1&attribute_id=22&file_no=12022-08-29