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On the geometry of point correspondences of three conformal spaces

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Abstract

Point correspondences of three conformal spaces are studied on the base of G. F. Laptev’s invariant methods. We establish the basic equations and geometrical objects of the point correspondences in question. We construct invariant normalizations of the spaces, single out the basic tensors of the correspondences, establish a connection of the correspondences with the theory of multidimensional 3-webs, and find the torsion and the curvature tensors of a point correspondence. For a series of particular cases, we prove existence theorems.

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References

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Authors and Affiliations

  1. Orenburg State Pedagogical University, ul. Sovetskaya 19, Orenburg, 460014, Russia

    V. S. Bolodurin

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  1. V. S. Bolodurin
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Correspondence to V. S. Bolodurin.

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Original Russian Text © V.S. Bolodurin, 2012, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, No. 8, pp. 3–14.

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Bolodurin, V.S. On the geometry of point correspondences of three conformal spaces. Russ Math. 56, 1–10 (2012). https://doi.org/10.3103/S1066369X12080014

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  • DOI: https://doi.org/10.3103/S1066369X12080014

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