A conformal transformation of certain contact Riemannian manifolds

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...

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...

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. ...

On Riemannian manifolds endowed with a locally conformal cosymplectic structure

We deal with a locally conformal cosymplectic manifoldM(φ,Ω,ξ,η,g) admitting a conformal contact quasi-torse-forming vector field T . The presymplectic 2-form Ω is a locally conformal cosymplectic 2-form. It is shown that T is a 3-exterior concurrent vector field. Infinitesimal transformations of the Lie algebra of ∧M are investigated. The Gauss map of the hypersurfaceMξ normal to ξ is conforma...

The Conformal Transformation Group of a Compact Homogeneous Riemannian Manifold