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On the spectral geometry of a Riemannian Legendre foliation
spectral geometry Riemannian Legendre foliation
2010/12/8
We obtain geometric characterizations of isospectral minimal Riemannian Legendre foliations on compact Sasakian manifolds of constant '-sectional curvature.
2-plectic geometry, Courant algebroids, and categorified prequantization
2-plectic geometry Courant algebroids categorified prequantization
2010/12/7
A 2-plectic manifold is a manifold equipped with a closed nondegenerate 3-form, just as a symplectic manifold is equipped with a closed nondegenerate 2-form. In 2-plectic geometry we meet higher analo...
The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry
almost-Riemannian geometry conjugate and cut loci
2010/12/6
We study the tangential case in 2-dimensional almost-Riemannian geometry. We analyse the connection with the Martinet case in sub-Rieman-nian geometry. We compute estimations of the exponential map wh...
Conformal geometry of surfaces in the Lagrangian--Grassmannian and second order PDE
Conformal geometry of surfaces Lagrangian--Grassmannian and second order PDE
2010/12/1
Of all real Lagrangian{Grassmannians LG(n; 2n), only LG(2; 4) admits a distinguished Lorentzian) conformal structure and hence is identi ed with the inde nite Mobius space S1;2.
We describe a family of calibrations arising naturally on a hyperk¨ahler manifoldM. These calibrations calibrate the holomorphic Lagrangian,holomorphic isotropic and holomorphic coisotropic subvarieti...
Quantum Isometries of the finite noncommutative geometry of the Standard Model
Quantum Isometries finite noncommutative geometry Standard Model
2010/12/6
We compute the quantum isometry group of the finite noncommutative geometry F describing
the internal degrees of freedom in the Standard Model of particle physics. We show that this
provides genuine...
Topological expansion of beta-ensemble model and quantum algebraic geometry in the sectorwise approach
Topological expansion of beta-ensemble model quantum algebraic geometry sectorwise approach
2010/12/14
We solve the loop equations of the β-ensemble model analogously to the solution found for the Hermitian matrices β = 1. For β = 1, the solution was expressed using the algebraic spectral curve of equa...
Quantum Statistical Mechanics, L-series and Anabelian Geometry
Arithmetic equivalence quantum statistical mechanics Bost-Connes system anabelian geometry
2010/11/29
It is known that two number fields with the same Dedekind zeta function are not necessarily
isomorphic. The zeta function of a number field can be interpreted as the partition function of
an associa...
Representation stacks, D-branes and noncommutative geometry
Representation stacks D-branes noncommutative geometry
2010/12/13
n this note we prove that the spec(C)-points of the representation Artin-stack [repnR/PGLn] of n-dimensional representations of an affine C-algebra R correspond to C-algebra morphisms R - An where An ...
One considers the monistic conception of a geometry, where there is only one fundamental quantity (world function). All other geometrical quantities a derivative quantities (functions of the world fun...
Coupling solutions of BGG-equations in conformal spin geometry
overdetermined systems conformal spin geometry twistor spinors conformal Killing fields conformal Killing forms
2010/12/1
BGG-equations are geometric overdetermined systems of PDEs on parabolic geometries. Normal solutions of BGG-equations are particularly interesting and we give a simple formula for the necessary and su...
Almost commutative Riemannian geometry, I: wave operators
noncommutative geometry quantum groups quantum gravity
2010/12/3
Associated to any (pseudo)-Riemannian manifold M of dimension n is an n + 1-dimensional noncommutative di erential structure (1; d)on the manifold.
In this paper we establish three basic equations for a general soliton structure on the Riemannian manifold (M, h , i). We then draw some geometric conclusions with the aid of the maximum principle.
Restrictions on the geometry of the periodic vorticity equation
Non-metric Euler equation geodesic flow diffeomor-phism group of the circle
2010/11/30
We prove that several evolution equations arising as mathematical models for fluid motion cannot be realized as metric Euler equations on the Lie group Diff1(S1) of all smooth and orientation-preservi...
A theorem of Lawson and Simons states that the only stable minimal submanifolds in CPn are complex submanifolds. We generalize their result to the cases of HPn and OP2. Our approach gives a unified vi...