# Foliated Cobordism and Motion

@article{Delphenich2002FoliatedCA, title={Foliated Cobordism and Motion}, author={David Henry Delphenich}, journal={arXiv: General Relativity and Quantum Cosmology}, year={2002} }

The mathematical notion of foliated cobordism is presented, and its relationship to both the motion of extended particles and wave motion is detailed. The fact that wave motion, when represented in such a manner on a four-dimensional spacetime, leads to a reduction of the bundle of linear frames to an SO(2)-principle bundle is demonstrated. Invariants of foliated cobordism are discussed as they relate to the aforementioned cases of motion.

## 5 Citations

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## References

SHOWING 1-10 OF 23 REFERENCES

Topology change and monopole creation.

- MathematicsPhysical review. D, Particles and fields
- 1986

It is shown that the condition for a topological cobordism to admit an appropriate metric is different in even and odd dimensions, which means that pair creation of Kaluza-Klein monopoles cannot occur via the mechanism considered.

Topological methods in hydrodynamics

- Mathematics
- 1998

A group theoretical approach to hydrodynamics considers hydrodynamics to be the differential geometry of diffeomorphism groups. The principle of least action implies that the motion of a fluid is…

Topology in general relativity

- Mathematics
- 1967

A number of theorems and definitions which are useful in the global analysis of relativistic world models are presented. It is shown in particular that, under certain conditions, changes in the…

Geometry of Foliations

- Mathematics
- 1997

1 Examples and Definition of Foliations.- 2 Foliations of Codimension One.- 3 Holonomy, Second Fundamental Form, Mean Curvature.- 4 Basic Forms, Spectral Sequence, Characteristic Form.- 5 Transversal…

The Hamilton-Cartan formalism in the calculus of variations

- Mathematics
- 1973

In this paper, we give an exposition of the geometry of the calculus of variations in several variables. The main emphasis is on the Hamiltonian formalism via the use of a linear differential form…

Spatially integrable space-times

- Mathematics
- 1974

The topological and geometrical restrictions on spatially integrable space-times foliated by space-like hypersurfaces are investigated.

Calculus of variations and partial differential equations of the first order

- Mathematics
- 1965

Continuous convergence, implicit functions, ordinary differential equations Fields of curves and multidimensional surfaces, complete systems Partial differential equations of the first order, theory…

Topics on space-time geometry

- Mathematics, Physics
- 1974

Several topics in the geometry of space-times are discussed, including the time and space-distributions of the space-time and a geometrical definition of singularities.

Exterior Differential Systems

- Mathematics
- 1990

Basic theorems Cartan-Khler theory linear differential systems the characteristic variety prolongation theory applications of commutative algebra and algebraic geometry to the study of exterior…