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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 reductive...

Self-duality and pointwise Osserman manifolds

Dimitri V. Alekseevsky; Novica Blažić; Neda Bokan; Zoran Rakić — 1999

Archivum Mathematicum

This paper is a contribution to the mathematical modelling of the hump effect. We present a mathematical study (existence, homogenization) of a Hamilton-Jacobi problem which represents the propagation of a front flame in a striated media.

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