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Grassmann image of non-isotropic surface of pseudo-Euclidean space

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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.

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Authors and Affiliations

  1. Zaporizhia National University, ul. Zhukovskogo 66, Zaporizhia, 69600, Ukraine

    P. G. Stegantseva & M. A. Grechneva

Authors
  1. P. G. Stegantseva
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  2. M. A. Grechneva
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Corresponding author

Correspondence to P. G. Stegantseva.

Additional information

Original Russian Text ©P.G. Stegantseva, M.A. Grechneva, 2017, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2017, No. 2, pp. 65–75.

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Stegantseva, P.G., Grechneva, M.A. Grassmann image of non-isotropic surface of pseudo-Euclidean space. Russ Math. 61, 55–63 (2017). https://doi.org/10.3103/S1066369X17020074

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  • DOI: https://doi.org/10.3103/S1066369X17020074

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