Naturally reductive metrics on homogeneous systems

Connections on Naturally Reductive

Connections on Naturally Reductive Spaces, Their Dirac Operator and Homogeneous Models in String Theory

Given a reductive homogeneous space M = G/H endowed with a naturally reductive metric, we study the one-parameter family of connections ∇t joining the canonical and the LeviCivita connection (t = 0, 1/2). We show that the Dirac operator Dt corresponding to t = 1/3 is the so-called “cubic” Dirac operator recently introduced by B. Kostant, and derive the formula for its square for any t, thus gen...

Einstein Metrics on Compact Lie Groups Which Are Not Naturally Reductive

The study of left-invariant Einstein metrics on compact Lie groups which are naturally reductive was initiated by J. E. D’Atri and W. Ziller in 1979. In the present work we prove existence of non-naturally reductive Einstein metrics on the compact simple Lie groups SO(n) (n ≥ 11), Sp(n) (n ≥ 3), E6, E7, and E8.

Direct Search Methods on Reductive Homogeneous Spaces

Direct search methods are mainly designed for use in problems with no equality constraints. However, there are many instances where the feasible set is of measure zero in the ambient space and no mesh point lies within it. There are methods for working with feasible sets that are (Riemannian) manifolds, but not all manifolds are created equal. In particular, reductive homogeneous spaces seem to...

Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three

We determine, for all three-dimensional non-unimodular Lie groups equipped with a Lorentzian metric, the set of homogeneous geodesics through a point. Together with the results of [C] and [CM2], this leads to the full classification of three-dimensional Lorentzian g.o. spaces and naturally reductive spaces.