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Grant support

Research of the two first named authors was partially supported by a MEC-FEDER grant MTM2017-89677-P. Research of the third named author was partially supported by a MECD grant FPU16/03096.

Analysis of institutional authors

Castro-Infantes, JesúsAuthor

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Curves in the Lorentz-Minkowski plane: elasticae, catenaries and grim-reapers

Publicated to:Open Mathematics. 16 747-766 - 2018-07-17 16(), DOI: 10.1515/math-2018-0069

Authors: Castro, Ildefonso; Castro-Infantes, Ildefonso; Castro-Infantes, Jesus

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Abstract

This article is motivated by a problem posed by David A. Singer in 1999 and by the classical Euler elastic curves. We study spacelike and timelike curves in the Lorentz-Minkowski plane L-2 whose curvature is expressed in terms of the Lorentzian pseudodistance to fixed geodesics. In this way, we get a complete description of all the elastic curves in L-2 and provide the Lorentzian versions of catenaries and grimreaper curves. We show several uniqueness results for them in terms of their geometric linear momentum. In addition, we are able to get arc-length parametrizations of all the aforementioned curves and they are depicted graphically.

Keywords

CatenariesCurvatureCurvature dependsDistancElastic curvesGrim-reaper curveLorentzian curves

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Open Mathematics, and although the journal is classified in the quartile Q3 (Agencia WoS (JCR)), its regional focus and specialization in Mathematics, give it significant recognition in a specific niche of scientific knowledge at an international level.

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 1.15. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 14, 2024)

This information is reinforced by other indicators of the same type, which, although dynamic over time and dependent on the set of average global citations at the time of their calculation, consistently position the work at some point among the top 50% most cited in its field:

  • Field Citation Ratio (FCR) from Dimensions: 5.78 (source consulted: Dimensions Jun 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-06-08, the following number of citations:

  • WoS: 7
  • Scopus: 10

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-06-08:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 2 (PlumX).

It is essential to present evidence supporting full alignment with institutional principles and guidelines on Open Science and the Conservation and Dissemination of Intellectual Heritage. A clear example of this is:

  • The work has been submitted to a journal whose editorial policy allows open Open Access publication.

Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: Last Author (CASTRO INFANTES, JESUS).