Fiber preserving Killing vector fields of connection metric
I2M - Château-Gombert
39 rue Frédéric Joliot-Curie
13453 MARSEILLE cedex 13
Arash BAZDAR (Aix-Marseille Université)
Let $(M,g)$ be a differentiable Riemannian manifold, $K$ be a compact Lie group and $P$ be a principal $K$-bundle over $M$ endowed with a connection $A$. Fixing a bi invariant inner product on the Lie algebra $Lie(K)$, the connection $A$ and the metric $g$ define a Riemannian metric $g_A$ on $P$. We give a decomposition theorem for fiber preserving Killing vector fields of $(P,g_A)$, in the case where $K$ is compact, connected and simple.
- Arash BAZDAR