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Proceedings Paper

A geometric Hamilton-Jacobi theory on a Nambu-Jacobi manifold

Publicated to:International Journal Of Geometric Methods In Modern Physics. 16 - 2019-02-01 16(), DOI: 10.1142/S0219887819400073

Authors: De León M; Sardón C

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Abstract

In this paper, we propose a geometric Hamilton-Jacobi (HJ) theory on a Nambu-Jacobi (NJ) manifold. The advantage of a geometric HJ theory is that if a Hamiltonian vector field XH can be projected into a configuration manifold by means of a one-form dW, then the integral curves of the projected vector field XHdW can be transformed into integral curves of the vector field XH provided that dW is a solution of the HJ equation. This procedure allows us to reduce the dynamics to a lower-dimensional manifold in which we integrate the motion. On the other hand, the interest of a NJ structure resides in its role in the description of dynamics in terms of several Hamiltonian functions. It appears in fluid dynamics, for instance. Here, we derive an explicit expression for a geometric HJ equation on a NJ manifold and apply it to the third-order Riccati differential equation as an example.

Keywords

geometric hamilton-jacobi theorylagrangian submanifoldsmechanicsnambu-jacobi manifoldorbitspoissonriccati equationssystemsGeometric hamilton-jacobi theoryLagrangian submanifoldsNambu-jacobi manifoldNambu-jacobi structureRiccati equations

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal International Journal Of Geometric Methods In Modern Physics, and although the journal is classified in the quartile Q3 (Agencia WoS (JCR)), its regional focus and specialization in Physics, Mathematical, 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 the Field Citation Ratio (FCR) of the Dimensions source, it yields a value of: 4.64, which 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: Dimensions Jun 2025)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-06-03, the following number of citations:

  • Scopus: 4
  • OpenCitations: 4

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 2025-06-03:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 1.
  • 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: 1 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 0.5.
  • The number of mentions on the social network X (formerly Twitter): 1 (Altmetric).

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.