Fiber preserving Killing vector fields of connection metric

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Date(s) - 08/10/2019
11 h 00 min - 12 h 00 min

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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.

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