Differential Geometry

  title={Differential Geometry},
  author={Michael E. Taylor},
1 Co-ordinate independent calculus. 2 1. 

Path problems in anisotropic regions


Geometry and Thermodynamics of Filament Bundles


Reductive Group Schemes

— We develop the relative theory of reductive group schemes, using dynamic techniques and algebraic spaces to streamline the original de-

Geometric approximation of curves and singularities of secant maps : a differential geometric approach

• local analysis: differential calculus. • global analysis: influence of local properties on the behavior of the entire curve.

Geometric Methods in Representation Theory

These are notes from the mini-course given by W. Schmid in June 2003 in the Brussels PQR2003 Euroschool.

On homogeneous Hermite-Lorentz spaces of low dimension

. We classify irreducible homogeneous almost Hermite-Lorentz spaces of complex dimension 3, and prove in particular they are geodesically complete.

Algebraicity of the image of period map

We prove that the image of period map is algebraic, as conjectured by Griffiths.

An Introduction to Riemannian Geometry: With Applications to Mechanics and Relativity

Differentiable Manifolds.- Differential Forms.- Riemannian Manifolds.- Curvature.- Geometric Mechanics.- Relativity.



Algebraic Topology

The focus of this paper is a proof of the Nielsen-Schreier Theorem, stating that every subgroup of a free group is free, using tools from algebraic topology.

Lectures on Riemann Surfaces

Contents: Covering Spaces.- Compact Riemann Surfaces.- Non-compact Riemann Surfaces.- Appendix.- References.- Symbol Index.- Author and Subject Index.

Nonlinear Methods in Riemannian and Kählerian Geometry

1. Geometric preliminaries.- 2. Some principles of analysis.- 3. The heat flow on manifolds. Existence and uniqueness of harmonic maps into nonpositively curved image manifolds.- 4. The parabolic

Differential forms in algebraic topology

This paper presents a meta-thesis on the basis of a model derived from the model developed in [Bouchut-Boyaval, M3AS (23) 2013] that states that the mode of action of the Higgs boson is determined by the modulus of the E-modulus.

Geometry of Manifolds

Manifolds Lie groups Fibre bundles Differential forms Connexions Affine connexions Riemannian manifolds Geodesics and complete Riemannian manifolds Riemannian curvature Immersions and the second

Differential Geometry: Curves - Surfaces - Manifolds

* Notations and prerequisites from analysis* Curves in $\mathbb{R}^n$* The local theory of surfaces* The intrinsic geometry of surfaces* Riemannian manifolds* The curvature tensor* Spaces of constant

Mathematical Methods of Classical Mechanics

Part 1 Newtonian mechanics: experimental facts investigation of the equations of motion. Part 2 Lagrangian mechanics: variational principles Lagrangian mechanics on manifolds oscillations rigid

Multiple Integrals in the Calculus of Variations

Semi-classical results.- The spaces Hmp and Hmp0.- Existence theorems.- Differentiability of weak solutions.- Regularity theorems for the solutions of general elliptic systems and boundary value

Teichmüller Theory in Riemannian Geometry

0 Mathematical Preliminaries.- 1 The Manifolds of Teichmuller Theory.- 1.1 The Manifolds A and As.- 1.2 The Riemannian Manifolds M and Ms.- 1.3 The Diffeomorphism Ms /? s ? As.- 1.4 Some Differential