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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
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Lie algebra bundle associated to a Lie group bundle
Refer the paper by Basavavannappa S KIRANAGI(B S KIRANAGI) on Lie Algebra Bundles, Bull. Sci. Math.2 series, 102(1978), 57-62. there are many papers by him.