A note on the uniqueness of the canonical connection of a naturally reductive space

OLMOS, CARLOS AND REGGIANI, SILVIO

MONATSHEFETE FUR MATHEMATIK

SPRINGER WIEN

Lugar: Viena; Año: 2013 vol. 172 p. 379 - 386

0026-9255

We extend the result in J. Reine Angew. Math. 664, 29-53, to the non-compact case. Namely, we prove that the canonical connection on a simply connected and irreducible naturally reductive space is unique, provided the space is not a sphere, a compact Lie group with a bi-invariant metric or its symmetric dual. In particular, the canonical connection is unique for the hyperbolic space when the dimension is different from three. We also prove that the canonical connection on the sphere is unique for the symmetric presentation. Finally, we compute the full isometry group (connected component) of a compact and locally irreducible naturally reductive space. DOI 10.1007/s00605-013-0554-6