Riemannian manifolds admitting a certain conformal transformation group

The Conformal Transformation Group of a Compact Homogeneous Riemannian Manifold

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. ...

Maximal Complexifications of Certain Homogeneous Riemannian Manifolds

Let M = G/K be a homogeneous Riemannian manifold with dimCGC = dimRG, where GC denotes the universal complexification of G. Under certain extensibility assumptions on the geodesic flow of M , we give a characterization of the maximal domain of definition in TM for the adapted complex structure and show that it is unique. For instance, this can be done for generalized Heisenberg groups and natur...

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 ...

Maximal Complexifications of Certain Riemannian Homogeneous Manifolds

Let M = G/K be a Riemannian homogeneous manifold with dimCG C = dimRG , where G C denotes the universal complexification of G. Under certain extensibility assumptions on the geodesic flow of M , we give a characterization of the maximal domain of definition in TM for the adapted complex structure and show that it is unique. For instance, this can be done for generalized Heisenberg groups and na...