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Lectures on Holomorphic Curves in Symplectic and Contact Geometry
Holomorphic Curves Symplectic Contact Geometry
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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...
Monistic conception of geometry
Monistic conception geometry
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2010/12/6
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...
On the Geometry of complete Ricci Solitons
Geometry complete Ricci Solitons
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2010/12/1
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.
Thermodynamic Geometry and Hawking Radiation
Quantum Gravity Hawking Radiation Horizon Perturbations Vaidya Geometry
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2010/12/15
This work explores the role of thermodynamic fluctuations in the two parameter Hawking adiating
black hole configurations. The system is characterized by an ensemble of arbitrary mass and radiation f...
Cyclic polygons in classical geometry
cyclic polygon Euclidean geometry hyperbolic geometry spherical geometry
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2010/12/7
Formulas about the side lengths, diagonal lengths or radius of the circumcircle of a cyclic polygon in Euclidean geometry, hyperbolic geometry or spherical geometry can be unified.
Graded geometry and Poisson reduction
Graded geometry Poisson reduction
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2010/12/1
A result of [2] extends the Marsden-Ratiu reduction theorem [4] in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry ne...