Two-dimensional nonisotropic surfaces with flat normal connection and a nondegenerate Grassmann image of constant curvature in the Minkowski space
UDC 514.764 We find possible values of  curvature of the Grassmann manifold along the  planes tangential to the Grassmann image of a two-dimensional nonisotropic surface with flat normal connection in the four-dimensional Minkowski space. It is shown that if th...
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| Date: | 2024 |
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| Main Authors: | , , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2024
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/6743 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 514.764
We find possible values of  curvature of the Grassmann manifold along the  planes tangential to the Grassmann image of a two-dimensional nonisotropic surface with flat normal connection in the four-dimensional Minkowski space. It is shown that if the surface with  flat normal connection is time-like, then the analyzed curvature may take values from the set $[0,1].$ However, if the surface with flat normal connection is space-like, then this curvature may take values from $(-\infty,-1]$ in the case of a space-like Grassmann image or the values from $[0,\infty)$ in the case of a time-like Grassmann image. The existence of two-dimensional nonisotropic surfaces with flat normal connection and constant curvature of their Grassmann image is proved for all values of curvature from the obtained sets. |
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| DOI: | 10.3842/umzh.v74i4.6743 |