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Moment maps, monodromy and mirror manifolds [PDF]

open access: greenSymplectic Geometry and Mirror Symmetry, 2001
Via considerations of symplectic reduction, monodromy, mirror symmetry and Chern-Simons functionals, a conjecture is proposed on the existence of special Lagrangians in the hamiltonian deformation class of a given Lagrangian submanifold of a Calabi-Yau manifold.
Richard Thomas
openalex   +3 more sources

Symmetric space valued moment maps [PDF]

open access: bronzePacific Journal of Mathematics, 2003
It is well known that we have three momentum map theories, or at least three natural \(G\)-spaces which serve as targets for moment maps: \(\mathfrak{g}^*\) for the classical Hamiltonian theory, \(G\) for the \(q\)-Hamiltonian theory and \(G_\mathbb{C}/G\) representing the Poisson or \(Y\)-valued theory.
Matthew Leingang
openalex   +3 more sources

Differentiability of quantum moment maps [PDF]

open access: green, 2002
We study quantum moment maps of $G$-invariant star products, which are a quantum analogue of the moment map for classical Hamiltonian systems. Introducing an integral representation, we show that any quantum moment map for a $G$-invariant star product is differentiable.
Kentaro Hamachi
openalex   +3 more sources

Mean Curvature Flow, Orbits, Moment Maps [PDF]

open access: greenTransactions of the American Mathematical Society, 2002
Given a compact Riemannian manifold together with a group of isometries, we discuss MCF of the orbits and some applications: e.g., finding minimal orbits. We then specialize to Lagrangian orbits in Kaehler manifolds. In particular, in the Kaehler-Einstein case we find a relation between MCF and moment maps which, for example, proves that the minimal ...
Tommaso Pacini
openalex   +8 more sources

A remark on the moment map [PDF]

open access: bronzeProceedings of the American Mathematical Society, 1994
Following S. Lie, it is proposed that moment maps be constructed for degenerate forms and the utility of such maps is illustrated by computing the moment maps for torus actions on C n {{\mathbf {C}}^n} and U ( n )
H. Azad
openalex   +2 more sources

Courant morphisms and moment maps [PDF]

open access: greenMathematical Research Letters, 2008
18 pages. v2: Minor corrections, one example (Example 2.11) added. v3: Remark 2.5 fixed. To appear in Math.
Henrique Bursztyn   +2 more
openalex   +5 more sources

Investigation of seismic parameters, calculation of Seismic moment and Geologic moment Kopeh-Dagh zone in Northeast of Iran [PDF]

open access: yesمخاطرات محیط طبیعی, 2021
The Kopeh-Dagh zone is the northern deformation zone due to the convergence of the Arabian and Eurasian plates Which forms an active area with a northwest-southeast trend.
Hadi Alinia, Mohammad Mahdi Khatib
doaj   +1 more source

Generic simplicity of quantum Hamiltonian reductions

open access: yesComptes Rendus. Mathématique, 2021
Let a reductive group $G$ act on a smooth affine complex algebraic variety $X.$ Let $\mathfrak{g}$ be the Lie algebra of $G$ and $\mu :T^*(X)\rightarrow \mathfrak{g}^*$ be the moment map.
Tikaradze, Akaki
doaj   +1 more source

Lie Group Statistics and Lie Group Machine Learning Based on Souriau Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as Generalized Casimir Invariant Function in Coadjoint Representation

open access: yesEntropy, 2020
In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their “space of evolution” associated to
Frédéric Barbaresco
doaj   +1 more source

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