Abstract.
We investigate a splitting of a short exact sequence of vector bundles with connection. We obtain an existence theorem of a unimodular splitting under a certain regularity condition on the fundamental form. In particular, we use a pseudo-inverse of the fundamental form to choose a canonical splitting, which is applied to an equiaffine immersion.
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Received: August 25, 2006. Revised: June 20, 2007.
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Abe, N., Ishii, R. A Splitting of Vector Bundles with Connection and Pseudo-Inverses of the Fundamental Form. Result. Math. 51, 181–195 (2008). https://doi.org/10.1007/s00025-007-0267-z
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DOI: https://doi.org/10.1007/s00025-007-0267-z