# Topics in Differential Geometry

@inproceedings{Michor2008TopicsID, title={Topics in Differential Geometry}, author={Peter W. Michor}, year={2008} }

Manifolds and vector fields Lie groups and group actions Differential forms and de Rham cohomology Bundles and connections Riemann manifolds Isometric group actions or Riemann $G$-manifolds Symplectic and Poisson geometry List of symbols Bibliography Index.

## 176 Citations

Riemannian foliation with exotic tori as leaves

- MathematicsBulletin of the London Mathematical Society
- 2019

We construct smooth fiber bundles such that the fibers are exotic tori and the total space has finite abelian fundamental group. This gives examples of a Riemannian foliation on a closed manifold…

Equivariant de Rham cohomology: theory and applications

- MathematicsSão Paulo Journal of Mathematical Sciences
- 2019

This is a survey on the equivariant cohomology of Lie group actions on manifolds, from the point of view of de Rham theory. Emphasis is put on the notion of equivariant formality, as well as on…

The Flow of Gauge Transformations on Riemannian Surface with Boundary

- Mathematics
- 2016

We consider the gauge transformations of a metric G-bundle over a compact Riemannian surface with boundary. By employing the heat flow method, the local existence and the long time existence of…

Optimal Symplectic Connections on Holomorphic Submersions

- MathematicsCommunications on Pure and Applied Mathematics
- 2020

The main result of this paper gives a new construction of extremal Kähler metrics on the total space of certain holomorphic submersions, giving a vast generalisation and unification of results of…

Hamiltonian structures for projectable dynamics on symplectic fiber bundles

- Mathematics, Physics
- 2012

The Hamiltonization problem for projectable vector fields on general symplectic fiber bundles is studied.
Necessary and sufficient conditions for the existence of Hamiltonian structures in the class…

Reductions of Dynamics on Second Iterated Bundles of Lie Groups

- Mathematics
- 2015

We consider trivializations of second iterated bundles of a Lie group that preserve lifted group structures. With such a trivialization, we elaborate Hamiltonian dynamics on cotangent, Lagrangian…

Hörmander's condition for normal bundles on spaces of immersions

- Mathematics
- 2015

Several representations of geometric shapes involve quotients of mapping spaces. The projection onto the quotient space defines two sub-bundles of the tangent bundle, called the horizontal and…

An 1-differentiable cohomology induced by a vector field

- Mathematics
- 2014

A new cohomology, induced by a vector field, is defined on pairs of differential forms (1– differentiable forms) in a manifold. It is proved a link with the classical de Rham cohomology and an…

DIFFERENTIAL GEOMETRY OF

- Mathematics
- 2011

As the third of our series of papers on differential geometry of microlinear Frolicher spaces is this paper devoted to the Frolicher-Nijenhuis calculus of their named bracket. The main result is that…

Variational calculus on Lie algebroids

- Mathematics
- 2006

It is shown that the Lagrange's equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of…

## References

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Curvature and Characteristic Classes

- Mathematics
- 1978

Differential forms and cohomology.- Multiplicativity. The simplicial de rham complex.- Connections in principal bundles.- The chern-weil homomorphism.- Topological bundles and classifying spaces.-…

Momentum Maps and Hamiltonian Reduction

- Mathematics
- 2003

Introduction.- Manifolds and smooth structures.- Lie group actions.- Pseudogroups and groupoids.- The standard momentum map.- Generalizations of the momentum map.- Regular symplectic reduction…

Differential Geometry, Lie Groups, and Symmetric Spaces

- Mathematics
- 1978

Elementary differential geometry Lie groups and Lie algebras Structure of semisimple Lie algebras Symmetric spaces Decomposition of symmetric spaces Symmetric spaces of the noncompact type Symmetric…

Lie Groupoids and Lie Algebroids in Differential Geometry

- Mathematics
- 1987

Introduction 1. The algebra of groupoids 2. Topological groupoids 3. Lie groupoids and Lie algebroids 4. The cohomology of Lie algebroids 5. An obstruction to the integrability of transitive Lie…

Lie groups, Lie algebras, and their representations

- Mathematics
- 1974

1 Differentiable and Analytic Manifolds.- 2 Lie Groups and Lie Algebras.- 3 Structure Theory.- 4 Complex Semisimple Lie Algebras And Lie Groups: Structure and Representation.

Lie group valued moment maps

- Mathematics
- 1997

We develop a theory of "quasi"-Hamiltonian G-spaces for which the moment map takes values in the group G itself rather than in the dual of the Lie algebra. The theory includes counterparts of…

Gauge Theory for Diffeomorphism Groups

- Mathematics
- 1988

We consider fibre bundles without structure group and develop the theory of connections, curvature, parallel transport, (nonlinear) frame bundle, the gauge group and it’s action on the space of…

Basic differential forms for actions of Lie groups. II

- Mathematics
- 1994

A section of a Riemannian G-manifold M is a closed submanifold Σ which meets each orbit orthogonally. It is shown that the algebra of G-invariant differential forms on M which are horizontal in the…

Natural operations in differential geometry

- Mathematics
- 1993

I. Manifolds and Lie Groups.- II. Differential Forms.- III. Bundles and Connections.- IV. Jets and Natural Bundles.- V. Finite Order Theorems.- VI. Methods for Finding Natural Operators.- VII.…

Lie Groups, Lie Algebras, Cohomology and some Applications in Physics

- Mathematics
- 1995

Preface 1. Lie groups, fibre bundles and Cartan calculus 2. Connections and characteristic classes 3. A first look at cohomology of groups and related topics 4. An introduction to abstract group…