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We study pure Yang–Mills theory on × S2, where is a compact Riemann surface, and invariance is assumed under rotations of S2. It is well known that the self-duality equations in this set-up reduce...
Quantum Gravity coupled to Matter via Noncommutative Geometry
Quantum Gravity Matter Noncommutative Geometry
2011/3/2
We show that the principal part of the Dirac Hamiltonian in 3+1 dimensions emerges in a semi-classical approximation from a construc-tion which encodes the kinematics of quantum gravity.
Classical integral geometry takes place in Rn equipped with the Euclidean metric. We begin to develop integral geometry for Rn equipped with the taxicab metric (induced by the 1-norm).
Tracing light propagation to the intrinsic accuracy of space-time geometry
relativity gravitation space-time geometry weak field approximations light propagation
2011/3/4
Advancement in astronomical observations and technical instrumentation requires coding light
propagation at high level of precision; this could open a new detection window of many subtle relativistic...
Weakly regular T2 symmetric spacetimes. The global geometry of future developments
regular T2 symmetric spacetimes global geometry future developments
2011/3/4
Under weak regularity assumptions, only, we develop a fully geometric theory of vacuum
Einstein spacetimes with T2–symmetry, establish the global well-posedness of the initial value
problem for Eins...
Weakly regular T2 symmetric spacetimes. The global geometry of future developments
regular T2 symmetric spacetimes global geometry of future developments
2011/3/4
Under weak regularity assumptions, only, we develop a fully geometric theory of vacuum
Einstein spacetimes with T2–symmetry, establish the global well-posedness of the initial value
problem for Eins...
Virial Theorem and Hypervirial Theorem in a spherical geometry
Viral Theorem Perturbation Theory Spherical geometry
2011/2/25
In the paper, we obtain the Virial Theorem and Hypervirial Theorem in a spherical geometry.
The Hypervirial Theorem and Hellmann-Feynman Theorem are used to formulate a perturbation
theorem without ...
Basic Riemannian Geometry and Sobolev Estimates used in Symplectic Topology
Basic Riemannian Geometry Sobolev Estimates used Symplectic Topology
2011/2/22
This note collects a number of standard statements in Riemannian geometry and in Sobolevspace
theory that play a prominent role in analytic approaches to symplectic topology. These
include relations...
We use the CR geometry of the standard hyperquadric in complex projective three-space to give a detailed twistor description of conformal foliations in Euclidean three-space.
On Hermitian manifolds, the second Ricci curvature tensors of various metric connectionsare closely related to the geometry of Hermitian manifolds. By refining the Bochnerformulas for any Hermitian co...
Scheme of lines on a family of 2-dimensional quadrics: geometry and derived category
2-dimensional quadrics geometry derived category
2010/11/23
Given a generic family $Q$ of 2-dimensional quadrics over a smooth 3-dimensional base $Y$ we consider the relative Fano scheme $M$ of lines of it. The scheme $M$ has a structure of a generically coni...
Tetrad gravity, electroweak geometry and conformal symmetry
Tetrad gravity 2-spinors electroweak geometry conformal symmetry dilaton
2010/12/3
A partly original description of gauge fields and electroweak geometry is proposed. A discussion of the breaking of conformal symmetry and the nature of the dilaton in the proposed setting indicates t...
By refining the Bochner formulas for any Hermitian complex vector bundle with an arbitrary metric connection over a compact Hermitian manifold, we can kill torsion and derive various vanishing theore...
We study the holomorphic unitary representations of the Jacobi group based on Siegel-Jacobi domains. Explicit polynomial orthonormal bases of the Fock spaces based on the Siegel-Jacobi disk are obtain...
Lectures on Holomorphic Curves in Symplectic and Contact Geometry
Holomorphic Curves Symplectic Contact Geometry
2010/11/12
This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incom...