Is it possible to have a non-split short exact sequences of vector bundles (on some smooth variety) $0\rightarrow V_1 \rightarrow V_2 \rightarrow V_3 \rightarrow 0$. Such that $V_2\cong V_1\oplus V_3$ as vector bundles?
Can non-split extension be isomorphic to the split one as objects
user127776
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