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Differential Geometry of Manifolds

2026 №57 (1)

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Kretov M.V. Kretova E.M.

On a subclass of ellipsoid complexes that admits a non-integral representation

DOI
10.5922/0321-4796-2026-57-1-5
Pages
64-75
manifold complex reference point ellipsoid affine spa­ce indicatrix focal manifold non-integral representation

Abstract

Using the group-theoretic method of differential geometric re­search by G. F. Laptev, as well as the methodology of scientific re­search on differential geometry by V. S. Malakhovsky, the study of complexes (three-parameter families) of ellipsoids with special pro­perties of differentiable maps associated with them in a three-di­mensional affine space. The complex of ellipsoids is considered as an image of the corresponding mapping. A subclass of previous­ly studied ellipsoid complexes is investigated when the difference indicatrix of the second and third coordinate vectors is a straight line parallel to the first coordinate vector. Interesting geo­metric properties of the studied manifold are found, which make it possi­ble to construct it, that is, to find its integral representation.

Reference

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