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A Lorentzian Quantum Geometry
Lorentzian Quantum Geometry Differential Geometry
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2011/9/1
Abstract: We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-tim...
Supergravity as Generalised Geometry I: Type II Theories
Supergravity Generalised Geometry I High Energy Physics - Theory
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2011/9/30
Abstract: We reformulate ten-dimensional type II supergravity as a generalised geometrical analogue of Einstein gravity, defined by an $O(9,1)\times O(1,9)\subset O(10,10)\times\bbR^+$ structure on th...
Schrodinger equations, deformation theory and $tt^*$-geometry
Schrodinger equations deformation theory Differential Geometry
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2011/8/26
Abstract: This is the first of a series of papers to construct the deformation theory of the form Schr\"odinger equation, which is related to a section-bundle system $(M,g,f)$, where $(M,g)$ is a nonc...
The geometry of embedded pseudo-Riemannian surfaces in terms of Poisson brackets
pseudo-Riemannian manifolds embedded surfaces Poisson brackets
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2011/8/25
Abstract: Arnlind, Hoppe and Huisken showed how to express the Gauss and mean curvature of a surface embedded in a Riemannian manifold in terms of Poisson brackets of the embedding coordinates. We gen...
Geometry of warped products
Geometry of warped products Differential Geometry
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2011/8/23
Abstract: This is a survey on the geometry of warped products, without, or essentially with only soft, calculation. Somewhere in the paper, the goal was to give a synthetic account since existing appr...
Basic coordinate-free non-Euclidean geometry
Basic coordinate-free non-Euclidean geometry Differential Geometry
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2011/8/23
Abstract: These lecture notes are based on [arXiv: math/0702714, 0907.4469, 0907.4470]. We introduce and study basic aspects of non-Euclidean geometries from a coordinate-free viewpoint.
How Geometry Controls the Tearing of Adhesive Thin Films on Curved Surfaces
Geometry Controls Curved Surfaces Adhesive Thin Films Tearing
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2011/7/7
Flaps can be detached from a thin film glued on a solid substrate by tearing and peeling. For flat substrates, it has been shown that these flaps spontaneously narrow and collapse in pointy triangular...
Exceptional collections on toric Fano threefolds and birational geometry
Exceptional collections toric Fano threefolds birational geometry
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2011/2/22
Bernardi and Tirabassi show the existence of a full strong excep-tional collection consisting of line bundles on smooth toric Fano 3-folds under assuming Bondal’s conjecture, which states that the Fro...
Infinite bubbling in non-Kählerian geometry
Infinite non-Kä hlerian geometry
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2011/2/25
In a holomorphic family (Xb)b∈B of non-K¨ahlerian compact manifolds,the holomorphic curves representing a fixed 2-homology class do not form a proper family in general.
Gauge fixing in (2+1)-gravity: Dirac bracket and spacetime geometry
Gauge fixing (2+1)-gravity: Dirac bracket spacetime geometry
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2011/3/2
We consider (2+1)-gravity with vanishing cosmological constant as a constrained dynamical system. By applying Dirac’s gauge fixing procedure, we implement the constraints and determine the Dirac brack...
Line bundles and the Thom construction in noncommutative geometry
Line bundles Thom construction noncommutative geometry
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2011/1/19
The idea of a line bundle in classical geometry is transferred to noncommutative geometry by the idea of a Morita context. From this we can construct Z and N graded algebras, the Z graded algebra bein...
Geometry and Energy of Non-abelian Vortices
Geometry Energy of Non-abelian Vortices
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2011/3/4
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
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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.
Integral geometry for the taxicab metric
Integral geometry taxicab metric
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2011/3/1
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
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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...