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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, Number 2, Pages 65–75
(Mi ivm9209)
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This article is cited in 5 scientific papers (total 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.
Received: 27.07.2015
Citation:
P. G. Stegantseva, M. A. Grechneva, “Grassman image of non-isotropic surface of pseudo-euclidean space”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 2, 65–75; Russian Math. (Iz. VUZ), 61:2 (2017), 55–63
Linking options:
https://www.mathnet.ru/eng/ivm9209 https://www.mathnet.ru/eng/ivm/y2017/i2/p65
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Abstract page: | 163 | Full-text PDF : | 47 | References: | 38 | First page: | 6 |
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