Two-dimensional nonisotropic surfaces with flat normal connection and a nondegenerate Grassmann image of constant curvature in the Minkowski space

• Datum: 2024
• Hauptverfasser: Stegantseva, P., Grechneva, M., Стеганцева, Полина, Стєганцева, Поліна, Гречнєва, Марина
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2024
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/6743
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

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.