Abstract
In this paper, it is shown that if the Lie algebras of linear endomorphism fields of two vector bundles E and E′ are isomorphic, then E′ is isomorphic to E⊗L for some line bundle L. Analogous results are obtained for the endomorphism fields of vector bundles equipped with some structures (Riemann structure, symplectic structure, ...).
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References
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Lecomte, P.B.A. Note on the linear endomorphisms of a vector bundle. Manuscripta Math 32, 231–238 (1980). https://doi.org/10.1007/BF01299603
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DOI: https://doi.org/10.1007/BF01299603