A surface containing a line and a circle through each point is a quadric

DOI10.1007/s10711-012-9750-0zbMath1273.14077arXiv1110.2338OpenAlexW3100231268MaRDI QIDQ357854

Fedor Nilov, Mikhail Skopenkov

Publication date: 13 August 2013

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.2338

zbMATH Keywords

circleruled surfacecyclideconic bundlecircular surface

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26) Elementary problems in Euclidean geometries (51M04)

Related Items (8)

Incidences with Curves in ℝ d ⋮ On a system of fifth-order partial differential equations describing surfaces containing two families of circular arcs ⋮ Surfaces that are covered by two pencils of circles ⋮ Surfaces containing two circles through each point ⋮ Surfaces containing two circles through each point and decomposition of quaternionic matrices ⋮ Improved Bounds for Incidences Between Points and Circles ⋮ Surfaces containing two isotropic circles through each point ⋮ Incidences with curves in \(\mathbb{R}^d\)

Cites Work

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• The multiple conical surfaces
• Die windschiefen Kegelschnittflächen
• Surfaces with Orthogonal Families of Circles
• A Closed Surface of Genus One in E 3 Cannot Contain Seven Circles Through Each Point

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