Some generalizations of the shadow problem in the Lobachevsky space

DOI10.1007/s11253-021-01908-zzbMath1483.52008OpenAlexW3196596044MaRDI QIDQ2230614

A. V. Kostin

Publication date: 24 September 2021

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11253-021-01908-z

zbMATH Keywords

hyperbolic space\(m\)-convexityhoroball\(m\)-semiconvexityshadow problem

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Spherical and hyperbolic convexity (52A55) Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30)

Cites Work

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• Generalized convex envelopes of sets and the problem of shadow
• Isometric immersion in \(E^ 3\) of a convex domain of the Lobachevskij plane containing two horocycles
• Problem of shadow (complex case)
• Generalizations of the shadow problem
• Problem of shadow in the Lobachevskii space
• The problem of shadow for domains in Euclidean spaces
• Generalized convex sets and the problem of shadow
• Shadow's problem
• Asymptotic Lines on the Pseudo-Spherical Surfaces
• Smarandache Theorem in Hyperbolic Geometry

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