Displaying similar documents to “Conformal Fields and Stability.”

A note on conformal vector fields on a Riemannian manifold

Sharief Deshmukh, Falleh Al-Solamy (2014)

Colloquium Mathematicae

Similarity:

We consider an n-dimensional compact Riemannian manifold (M,g) and show that the presence of a non-Killing conformal vector field ξ on M that is also an eigenvector of the Laplacian operator acting on smooth vector fields with eigenvalue λ > 0, together with an upper bound on the energy of the vector field ξ, implies that M is isometric to the n-sphere Sⁿ(λ). We also introduce the notion of φ-analytic conformal vector fields, study their properties, and obtain a characterization of...

Uniqueness of the stereographic embedding

Michael Eastwood (2014)

Archivum Mathematicum

Similarity:

The standard conformal compactification of Euclidean space is the round sphere. We use conformal geodesics to give an elementary proof that this is the only possible conformal compactification.