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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2017 Number 2, Pages 65–75 (Mi ivm9209)

This article is cited in 5 papers

Grassman image of non-isotropic surface of pseudo-euclidean space

P. G. Stegantseva, M. A. Grechneva

Zaporizhia National University, 66 Zhukovskogo str., Zaporizhia, 69600 Ukraine

Abstract: 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.

UDC: 514.764

Received: 27.07.2015


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:2, 55–63

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© Steklov Math. Inst. of RAS, 2024