Special Issue "Applications of Differential Geometry"

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 31 October 2018

Special Issue Editor

Guest Editor
Prof. Dr. Anna Maria Fino

Dipartimento di Matematica“G. Peano”, Università di Torino, Turin 8-10124, Italy
Website | E-Mail
Interests: differential geometry; complex geometry; Lie groups; geometric flows

Special Issue Information

Dear Colleagues,

Differential geometry deals with the application of methods of local and global analysis to geometric problems. It was developed during the 18th and 19th century with the the theory of curves and surfaces in the three-dimensional Euvclidean space. From the 19th century it has grown, considering more generally geometric structures on differential manifolds.

It is deeply linked to other areas of mathematics, such as partial differential equations, topology, complex analytic functions, dynamical systems and group theory.

The goal of this Special Issue is to explore the multifaceted realm of differential geometry, providing a collection of research and survey papers that reflect the research in differential geometry and explore applications in other areas.

Indeed, differential geometry is, not only the standard language used to formulate general relativity, but it has found applications also in medical imaging, computer vision, Hamiltonian mechanics, geometrothermodynamics, geometric design, geometric control and information geometry.

We look forward to your contributions to this Special Issue,

Prof. Dr. Anna Maria Fino
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 350 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Riemannian geometry
  • Symplectic geometry
  • Contact geometry
  • Complex geometry
  • Geometric structures
  • Special geometries
  • Submanifold theory
  • Geometric flows
  • Finsler geometry
  • General relativity
  • String theory
  • Medical imaging
  • Computer vision
  • Hamiltonian mechanics
  • Geometrothermodynamics
  • Geometric design
  • Geometric Control
  • Information geometry

Published Papers (1 paper)

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Review

Open AccessReview Mathematical Modeling of Rogue Waves: A Survey of Recent and Emerging Mathematical Methods and Solutions
Received: 16 May 2018 / Revised: 6 June 2018 / Accepted: 8 June 2018 / Published: 20 June 2018
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Abstract
Anomalous waves and rogue events are closely associated with irregularities and unexpected events occurring at various levels of physics, such as in optics, in oceans and in the atmosphere. Mathematical modeling of rogue waves is a highly active field of research, which has
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Anomalous waves and rogue events are closely associated with irregularities and unexpected events occurring at various levels of physics, such as in optics, in oceans and in the atmosphere. Mathematical modeling of rogue waves is a highly active field of research, which has evolved over the last few decades into a specialized part of mathematical physics. The applications of the mathematical models for rogue events is directly relevant to technology development for the prediction of rogue ocean waves and for signal processing in quantum units. In this survey, a comprehensive perspective of the most recent developments of methods for representing rogue waves is given, along with discussion of the devised forms and solutions. The standard nonlinear Schrödinger equation, the Hirota equation, the MMT equation and other models are discussed and their properties highlighted. This survey shows that the most recent advancement in modeling rogue waves give models that can be used to establish methods for the prediction of rogue waves in open seas, which is important for the safety and activity of marine vessels and installations. The study further puts emphasis on the difference between the methods and how the resulting models form the basis for representing rogue waves in various forms, solitary or with a wave background. This review has also a pedagogic component directed towards students and interested non-experts and forms a complete survey of the most conventional and emerging methods published until recently. Full article
(This article belongs to the Special Issue Applications of Differential Geometry)
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