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Visual and hidden symmetry in geometry
Computers & Mathematics with Applications, 1989 AbstractA symmetry appears in modern geometry and its numerous applications both in explicit form (visually trivial) and sometimes, through sufficiently complex mathematical transformations, in veiled, hidden form. This current paper is made up of commentaries to a series of mathematical, graphical works of the author.
A. T. Fomenko
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The geometry underlying mirror symmetry [PDF]
, 1999 26 pages, AmS-LaTeX. Final version, to appear in Proc. European Algebraic Geometry Conference (Warwick, 1996)
David R. Morrison
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On the geometry of lambda-symmetries and PDE reduction [PDF]
Journal of Physics A: Mathematical and General, 2004 We give a geometrical characterization of $ $-prolongations of vector fields, and hence of $ $-symmetries of ODEs. This allows an extension to the case of PDEs and systems of PDEs; in this context the central object is a horizontal one-form $ $, and we speak of $ $-prolongations of vector fields and $ $-symmetries of PDEs.
Giuseppe Gaeta, Paola Morando
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The geometry of mirror symmetry
, 2005 11 pages of "Encyclopaedia of Mathematical Physics"
Richard P. Thomas
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T-Symmetry in String Geometry Theory
Advances in High Energy PhysicsString geometry theory is one of the candidates of nonperturbative formulation of string theory. In this paper, we have shown that dimensionally reduced string geometry theories have what we call T-symmetry.
Matsuo Sato, Taiki Tohshima
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Geometry-symmetry-free and material-symmetry-guaranteed polariton-induced transparency. [PDF]
iScienceSummary: Plasmon-induced transparency is a classical analogue of electromagnetically induced transparency (EIT). However, its realization and control primarily rely on geometry engineering rather than tuning plasmon polaritons (PPs) themselves, due to ...
Tang X +7 more
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Jet-determination of symmetries of parabolic geometries [PDF]
Mathematische Annalen, 2017 We establish 2-jet determinacy for the symmetry algebra of the underlying structure of any (complex or real) parabolic geometry. At non-flat points, we prove that the symmetry algebra is in fact 1-jet determined. Moreover, we prove 1-jet determinacy at any point for a variety of non-flat parabolic geometries - in particular torsion-free, parabolic ...
Boris Kruglikov, Dennis The
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Geometry and symmetry in skyrmion dynamics [PDF]
Physical Review B, 2021 The uniform motion of chiral magnetic skyrmions induced by a spin-transfer torque displays an intricate dependence on the skyrmions' topological charge and shape. We reveal surprising patterns in this dependence through simulations of the Landau-Lifshitz-Gilbert equation with Zhang-Li torque and explain them through a geometric analysis of Thiele's ...
Bernd J. Schroers +7 more
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On the Geometry of Symmetry Breaking Inequalities [PDF]
Mathematical Programming, 2021 Breaking symmetries is a popular way of speeding up the branch-and-bound method for symmetric integer programs. We study fundamental domains, which are minimal and closed symmetry breaking polyhedra. Our long-term goal is to understand the relationship between the complexity of such polyhedra and their symmetry breaking capability. Borrowing ideas from
José Verschae +2 more
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Weyl conformal geometry vs Weyl anomaly
Journal of High Energy Physics, 2023 Weyl conformal geometry is a gauge theory of scale invariance that naturally brings together the Standard Model (SM) and Einstein gravity. The SM embedding in this geometry is possible without new degrees of freedom beyond SM and Weyl geometry, while ...
D. M. Ghilencea
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