Displaying similar documents to “Homogeneous hessian manifolds”

Sobolev spaces of integer order on compact homogeneous manifolds and invariant differential operators

Cristiana Bondioli (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni


Let M be a Riemannian manifold, which possesses a transitive Lie group G of isometries. We suppose that G , and therefore M , are compact and connected. We characterize the Sobolev spaces W p 1 M 1 < p < + by means of the action of G on M . This characterization allows us to prove a regularity result for the solution of a second order differential equation on M by global techniques.

Metrics with homogeneous geodesics on flag manifolds

Dimitri V. Alekseevsky, Andreas Arvanitoyeorgos (2002)

Commentationes Mathematicae Universitatis Carolinae


A geodesic of a homogeneous Riemannian manifold ( M = G / K , g ) is called homogeneous if it is an orbit of an one-parameter subgroup of G . In the case when M = G / H is a naturally reductive space, that is the G -invariant metric g is defined by some non degenerate biinvariant symmetric bilinear form B , all geodesics of M are homogeneous. We consider the case when M = G / K is a flag manifold, i.eȧn adjoint orbit of a compact semisimple Lie group G , and we give a simple necessary condition that M admits a non-naturally...