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Reconstruction of a submanifold of Euclidean space from its Grassmannian image that degenerates into a line

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Abstract

We study the existence of a submanifoldF n of Euclidean spaceE n+p with prescribed Grassmannian image that degenerates into a line. We prove that Γ is the Grassmannian image of a regular submanifoldF n of Euclidean spaceE n+p if and only if the curve Γ in the Grassmann manifoldG + (p, n+p) is asymptoticallyC r-regular,r>1. HereG + (n, n+p) is embedded into the sphereS N,N=C p n+p =( n+p p ), by the Plücker coordinates.

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Authors and Affiliations

  1. Institute for Low Temperature Physics and Engineering, USSR

    V. A. Gor'kavyi

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  1. V. A. Gor'kavyi
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Translated fromMatematicheskie Zametki, Vol. 59, No. 5, pp. 681–691, May, 1996.

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Gor'kavyi, V.A. Reconstruction of a submanifold of Euclidean space from its Grassmannian image that degenerates into a line. Math Notes 59, 490–497 (1996). https://doi.org/10.1007/BF02308815

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  • DOI: https://doi.org/10.1007/BF02308815

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