Helicoidal minimal surfaces in the 3-sphere: an approach via spherical curves
Publicated to:Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas. 118 (2): 77- - 2024-04-01 118(2), DOI: 10.1007/s13398-024-01574-3
Authors: Castro, Ildefonso; Castro-Infantes, Ildefonso; Castro-Infantes, Jesus
Affiliations
Abstract
We prove an existence and uniqueness theorem about spherical helicoidal (in particular, rotational) surfaces with prescribed mean or Gaussian curvature in terms of a continuous function depending on the distance to its axis. As an application in the case of vanishing mean curvature, it is shown that the well-known conjugation between the belicoid and the catenoid in Euclidean three-space extends naturally to the 3-sphere to their spherical versions and determine in a quite explicit way their associated surfaces in the sense of Lawson. As a key tool, we use the notion of spherical angular momentum of the spherical curves that play the role of profile curves of the minimal helicoidal surfaces in the 3-sphere.
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Bibliometric impact. Analysis of the contribution and dissemination channel
The work has been published in the journal Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2024 there are still no calculated indicators, but in 2023, it was in position 53/483, thus managing to position itself as a Q1 (Primer Cuartil), in the category Mathematics.
Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.
Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2025-07-26:
- WoS: 1
- Scopus: 1
Impact and social visibility
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).