Geodesic
Grassman image of non-isotropic surface of pseudo-euclidean space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2017), pp. 65-75

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We consider submanifolds of non-isotropic planes of the Grassman manifold of the pseudo-Euclidean space. We prove a theorem about the unboundedness of the sectional curvature of the submanifolds of the two-dimensional non-isotropic planes of the four-dimensional pseudo-Euclidean space with the help of immersion in the six-dimensional pseudo-Euclidean space of index 3. We also introduce a concept of the indicatrix of normal curvature and study the properties of this indicatrix and the Grassman image of the non-isotropic surface of the pseudo-Euclidean space. We find a connection between the curvature of the Grassman image and the intrinsic geometry of the plane. We suggest the classification of the points of the Grassman image.
Keywords: pseudo-Euclidean space, Grassman manifold, sectional curvature, Grassman image of the surface, indicatrix of the normal curvature. 
@article{IVM_2017_2_a6,
     author = {P. G. Stegantseva and M. A. Grechneva},
     title = {Grassman image of non-isotropic surface of pseudo-euclidean space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {65--75},
     publisher = {mathdoc},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_2_a6/}
}
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P. G. Stegantseva; M. A. Grechneva. Grassman image of non-isotropic surface of pseudo-euclidean space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2017), pp. 65-75. http://geodesic.mathdoc.fr/item/IVM_2017_2_a6/