Geodesic orbit manifolds and Killing fields of constant length

Details Geodesic orbit manifolds and Killing fields of constant length Geodesic orbit manifolds and Killing fields of constant length

2011-04-14

arxiv.org/abs/1104.2664v2

Mathematics

Differential Geometry

7 pages, some typos are corrected

Scientific paper

The goal of this paper is to clarify connections between Killing fields of constant length on a Rimannian geodesic orbit manifold $(M,g)$ and the structure of its full isometry group. The Lie algebra of the full isometry group of $(M,g)$ is identified with the Lie algebra of Killing fields $\mathfrak{g}$ on $(M,g)$. We prove the following result: If $\mathfrak{a}$ is an abelian ideal of $\mathfrak{g}$, then every Killing field $X\in \mathfrak{a}$ has constant length. On the ground of this assertion we give a new proof of one result of C. Gordon: Every Riemannian geodesic orbit manifold of nonpositive Ricci curvature is a symmetric space.

Affiliated with

Also associated with

No associations

Rating

Geodesic orbit manifolds and Killing fields of constant length does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geodesic orbit manifolds and Killing fields of constant length, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geodesic orbit manifolds and Killing fields of constant length will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-165224