Some Remarks on the Hyperk\"ahler Reduction
Differential Geometry
2017-01-11 v1 Symplectic Geometry
Abstract
We consider a hyperk\"ahler reduction and describe it via frame bundles. Tracing the connection through the various reductions, we recover the results of Gocho and Nakajima. In addition, we show that the fibers of such a reduction are necessarily totally geodesic. As an independent result, we describe O'Neill's submersion tensors on principal bundles.
Cite
@article{arxiv.1701.02603,
title = {Some Remarks on the Hyperk\"ahler Reduction},
author = {Robin Raymond},
journal= {arXiv preprint arXiv:1701.02603},
year = {2017}
}
Comments
25 pages; comments are welcome