Discontinuous Normals in Non-Euclidean Geometries and Two-Dimensional Gravity

@article{Battista2022DiscontinuousNI,
  title={Discontinuous Normals in Non-Euclidean Geometries and Two-Dimensional Gravity},
  author={Emmanuele Battista and Giampiero Esposito},
  journal={Symmetry},
  year={2022},
  volume={14},
  pages={1979}
}
This paper builds two detailed examples of generalized normal in non-Euclidean spaces, i.e., the hyperbolic and elliptic geometries. In the hyperbolic plane we define a n-sided hyperbolic polygon P, which is the Euclidean closure of the hyperbolic plane H, bounded by n hyperbolic geodesic segments. The polygon P is built by considering the unique geodesic that connects the n+2 vertices z˜,z0,z1,...,zn−1,zn. The geodesics that link the vertices are Euclidean semicircles centred on the real axis… 

Figures from this paper

Geodesic motion in Euclidean Schwarzschild geometry

This paper performs a systematic investigation of geodesic motion in Euclidean Schwarzschild geometry, which is studied in the equatorial plane. The explicit form of geodesic motion is obtained in

References

SHOWING 1-10 OF 35 REFERENCES

Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions

A general method is known to exist for studying Abelian and non-Abelian gauge theories, as well as Euclidean quantum gravity, at 1-loop level on manifolds with boundary. In the latter case, boundary

A Note on Boundary Conditions in Euclidean Gravity

We review what is known about boundary conditions in General Relativity on a spacetime of Euclidean signature. The obvious Dirichlet boundary condition, in which one specifies the boundary geometry,

What is a reduced boundary in general relativity?

The concept of boundary plays an important role in several branches of general relativity, e.g., the variational principle for the Einstein equations, the event horizon and the apparent horizon of

Non-local boundary conditions in Euclidean quantum gravity

Non-local boundary conditions for Euclidean quantum gravity are proposed, consisting of an integro-differential boundary operator acting on metric perturbations. In this case, the operator P on

Geometry

The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of W ∞

Lack of strong ellipticity in Euclidean quantum gravity

Recent work in Euclidean quantum gravity has studied boundary conditions which are completely invariant under infinitesimal diffeomorphisms on metric perturbations. On using the de Donder

Local symmetries and constraints

The general relationship between local symmetries occurring in a Lagrangian formulation of a field theory and the corresponding constraints present in a phase space formulation are studied. First, a

Minimal surfaces and functions of bounded variation

I: Parametric Minimal Surfaces.- 1. Functions of Bounded Variation and Caccioppoli Sets.- 2. Traces of BV Functions.- 3. The Reduced Boundary.- 4. Regularity of the Reduced Boundary.- 5. Some