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

Fedor K. Nilov; Mikhail Skopenkov

doi:10.1007/s10711-012-9750-0

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

Fedor K. Nilov, Mikhail Skopenkov

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We prove that a surface in 3-dimensional Euclidean space containing a line and a circle through each point is a quadric. We also give some particular results on the classification of surfaces containing several circles through each point. © 2012 Springer Science+Business Media B.V.

Original language	English (US)
Pages (from-to)	301-310
Number of pages	10
Journal	Geometriae Dedicata
Volume	163
Issue number	1
DOIs	https://doi.org/10.1007/s10711-012-9750-0
State	Published - Jun 20 2012

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors were supported in part by President of the Russian Federation grant MK-3965.2012.1 and the program FCP-2012-1.2.2-12-000-1001-7779. The second author was supported in part by "Dynasty" foundation and Simons-IUM fellowship.

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s10711-012-9750-0

Cite this

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AU - Skopenkov, Mikhail

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PY - 2012/6/20

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N2 - We prove that a surface in 3-dimensional Euclidean space containing a line and a circle through each point is a quadric. We also give some particular results on the classification of surfaces containing several circles through each point. © 2012 Springer Science+Business Media B.V.

AB - We prove that a surface in 3-dimensional Euclidean space containing a line and a circle through each point is a quadric. We also give some particular results on the classification of surfaces containing several circles through each point. © 2012 Springer Science+Business Media B.V.

UR - http://hdl.handle.net/10754/562221

UR - http://arxiv.org/abs/arXiv:1110.2338v2

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

Abstract

Bibliographical note

ASJC Scopus subject areas

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