Envelopes of splines in the projective plane

Krzysztof Krakowski

doi:10.1093/imamci/dni014

Envelopes of splines in the projective plane

Krzysztof Krakowski

School of Science & Technology

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

6 Citations (Scopus)

Abstract

In this paper a family of curves - Riemannian cubics - in the unit sphere and the real projective plane is investigated. Riemannian cubics naturally arise as solutions to variational problems in Riemannian spaces. It is remarkable to find that an envelope of lines generated by a Riemannian cubic in one space is (nearly) a Riemannian cubic in another space.

Original language	English
Pages (from-to)	171-180
Journal	IMA Journal of Mathematical Control and Information
Volume	22
Issue number	2
DOIs	https://doi.org/10.1093/imamci/dni014
Publication status	Published - 2005

Keywords

Algebraic and Differential Geometry

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10.1093/imamci/dni014

https://hdl.handle.net/1959.11/3279

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AB - In this paper a family of curves - Riemannian cubics - in the unit sphere and the real projective plane is investigated. Riemannian cubics naturally arise as solutions to variational problems in Riemannian spaces. It is remarkable to find that an envelope of lines generated by a Riemannian cubic in one space is (nearly) a Riemannian cubic in another space.

KW - Algebraic and Differential Geometry

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DO - 10.1093/imamci/dni014

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JO - IMA Journal of Mathematical Control and Information

JF - IMA Journal of Mathematical Control and Information

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Envelopes of splines in the projective plane

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