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The geometry of mirror symmetry [PDF]

Encylopedia of mathematical physics (Eds: Francoise J, Naber GL, Tsou ST), Oxford, Elsevier, 2006, pages 439 -- 448., 2005
We give a brief survey of some of the geometry of mirror symmetry, written in 2004 for the "Encyclopaedia of Mathematical Physics". Probably a little bit out of date now in a few places, but hey.
Richard P. Thomas
arxiv   +5 more sources

Symmetries of Parabolic Geometries [PDF]

Differential Geometry and its Applications 27, No. 5, 2009, 605-622, 2009
We generalize the concept of affine locally symmetric spaces for parabolic geometries. We discuss mainly $|1|$--graded geometries and we show some restrictions on their curvature coming from the existence of symmetries. We use the theory of Weyl structures to discuss more interesting $|1|$--graded geometries which can carry a symmetry in a point with ...
Lenka Zalabová, Lenka Zalabová
arxiv   +5 more sources

Symmetry breaking in geometry [PDF]

arXiv, 2022
A geometric mechanism that may, in analogy to similar notions in physics, be considered as "symmetry breaking" in geometry is described, and several instances of this mechanism in differential geometry are discussed: it is shown how spontaneous symmetry breaking may occur, and it is discussed how explicit symmetry breaking may be used to tackle certain
Fuchs, Andreas, Hertrich-Jeromin, Udo, Pember, Mason   +2 more
arxiv   +3 more sources

Teleparallel Geometry with a Single Affine Symmetry [PDF]

J. Math. Phys. 64, 022503 (2023), 2022
In teleparallel geometries, symmetries are represented by affine frame symmetries which constrain both the (co)frame basis and the spin-connection (which are the primary geometric objects). In this paper we shall study teleparallel geometries with a single affine symmetry, utilizing the locally Lorentz covariant approach and adopting a complex null ...
A. A. Coley, R. J. van den Hoogen
arxiv   +3 more sources

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
openalex   +3 more sources

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
openalex   +4 more sources

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
openalex   +7 more sources

Kappa symmetry, generalized calibrations and spinorial geometry [PDF]

, 2006
We extend the spinorial geometry techniques developed for the solution of supergravity Killing spinor equations to the kappa symmetry condition for supersymmetric brane probe configurations in any supergravity background.
G. Papadopoulos, George Papadopoulos, J. Gillard, J. Gutowski, J.M. Figueroa-O'Farrill, J.P. Gauntlett, J.P. Gauntlett, L. Martucci, M. Marino, M.R. Douglas, P. Koerber, Peter Sloane, R. Bryant, R. Harvey, U. Gran, U. Gran, U. Gran, U. Gran, U. Gran   +18 more
core   +4 more sources

Symmetries in Riemann-Cartan Geometries [PDF]

SIGMA 20 (2024), 078, 20 pages
Riemann-Cartan geometries are geometries that admit non-zero curvature and torsion tensors. These geometries have been investigated as geometric frameworks for potential theories in physics including quantum gravity theories and have many important differences when compared to Riemannian geometries.
McNutt, David D., Coley, Alan A., Hoogen, Robert J. van den   +2 more
arxiv   +3 more sources

Gauge Symmetry, T-Duality and Doubled Geometry [PDF]

Journal of High Energy Physics, 2007
String compactifications with T-duality twists are revisited and the gauge algebra of the dimensionally reduced theories calculated. These reductions can be viewed as string theory on T-fold backgrounds, and can be formulated in a `doubled space' in ...
Hull, C. M., Reid-Edwards, R. A.
core   +6 more sources