The present paper aims to study the complete, horizontal and diagonal lifts of metallic structures in the cotangent bundle. Furthermore, the Nijenhuis tensor of a metallic structure is calculated and its integrability conditions by means of partial differential equations are established.
Download full-text PDF |
Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC11214461 | PMC |
| http://dx.doi.org/10.1016/j.heliyon.2024.e32144 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Novel theorems for the cotangent bundle endowed with metallic structures on a differentiable manifold.
Heliyon
June 2024
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586 Saudi Arabia.
The present paper aims to study the complete, horizontal and diagonal lifts of metallic structures in the cotangent bundle. Furthermore, the Nijenhuis tensor of a metallic structure is calculated and its integrability conditions by means of partial differential equations are established.
View Article and Find Full Text PDFReformulating scalar-tensor field theories as scalar-scalar field theories using a novel geometry.
Philos Trans A Math Phys Eng Sci
May 2022
Department of Applied Math, University of Waterloo, Waterloo, Ontario, Canada.
In this paper, I shall show how the notions of Finsler geometry can be used to construct a similar geometry using a scalar field, , on the cotangent bundle of a differentiable manifold . This will enable me to use the second vertical derivatives of , along with the differential of a scalar field on , to construct a Lorentzian metric on that depends upon . I refer to a field theory based upon a manifold with such a Lorentzian structure as a scalar-scalar field theory.
View Article and Find Full Text PDFLie polynomials and a twistorial correspondence for amplitudes.
Lett Math Phys
December 2021
The Mathematical Institute, University of Oxford, AWB, ROQ, Oxford, OX2 6GG UK.
We review Lie polynomials as a mathematical framework that underpins the structure of the so-called double copy relationship between gauge and gravity theories (and a network of other theories besides). We explain how Lie polynomials naturally arise in the geometry and cohomology of , the moduli space of points on the Riemann sphere up to Mobiüs transformation. We introduce a twistorial correspondence between the cotangent bundle , the bundle of forms with logarithmic singularities on the divisor as the twistor space, and the space of momentum invariants of massless particles subject to momentum conservation as the analogue of space-time.
View Article and Find Full Text PDFBlack-Scholes Theory and Diffusion Processes on the Cotangent Bundle of the Affine Group.
Entropy (Basel)
April 2020
Department of Mechanical Engineering, National University of Singapore, Singapore 117575, Singapore.
The Black-Scholes partial differential equation (PDE) from mathematical finance has been analysed extensively and it is well known that the equation can be reduced to a heat equation on Euclidean space by a logarithmic transformation of variables. However, an alternative interpretation is proposed in this paper by reframing the PDE as evolving on a Lie group. This equation can be transformed into a diffusion process and solved using mean and covariance propagation techniques developed previously in the context of solving Fokker-Planck equations on Lie groups.
View Article and Find Full Text PDFHalf conformally flat gradient Ricci almost solitons.
Proc Math Phys Eng Sci
May 2016
Faculty of Mathematics , University of Santiago de Compostela, 15782 Santiago de Compostela, Spain.
The local structure of half conformally flat gradient Ricci almost solitons is investigated, showing that they are locally conformally flat in a neighbourhood of any point where the gradient of the potential function is non-null. In opposition, if the gradient of the potential function is null, then the soliton is a steady traceless -Einstein soliton and is realized on the cotangent bundle of an affine surface.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!