Isometry to spheres of Riemannian manifolds admitting a conformal transformation group

The Conformal Transformation Group of a Compact Homogeneous Riemannian Manifold

ISOMETRY GROUPS OF k-CURVATURE HOMOGENEOUS PSEUDO-RIEMANNIAN MANIFOLDS

We study the isometry groups of a family of complete p + 2curvature homogeneous pseudo-Riemannian metrics on R which have neutral signature (3 + 2p, 3 + 2p), and which are 0-curvature modeled on an indecomposible symmetric space.

A Geometry Preserving Kernel over Riemannian Manifolds

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

The Isometry Group of a Riemannian Manifold with boundary

Riemannian Manifolds Admitting Isometric Immersions by Their First Eigenfunctions

Given a compact manifold M, we prove that every critical Riemannian metric g for the functional “first eigenvalue of the Laplacian” is λ1-minimal (i.e., (M, g) can be immersed isometrically in a sphere by its first eigenfunctions) and give a sufficient condition for a λ1-minimal metric to be critical. In the second part, we consider the case where M is the 2dimensional torus and prove that the ...