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1. • CommentRowNumber1.
   • CommentAuthorDexter Chua
   • CommentTimeAug 9th 2016
   • (edited Aug 9th 2016)
   • PermaLink
   Author: Dexter Chua
   Format: MarkdownItexAdded the definition of a [[exterior covariant derivative]] on a vector bundle, and reformatted the existing content (exterior covariant derivative on principal bundle). In Definition 1.7, does the induced external covariant derivative coincide with external covariant derivative in the sense of Definition 1.1 under the induced connection on the vector bundle? (EDIT: Yes.)

   Added the definition of a exterior covariant derivative on a vector bundle, and reformatted the existing content (exterior covariant derivative on principal bundle).

   In Definition 1.7, does the induced external covariant derivative coincide with external covariant derivative in the sense of Definition 1.1 under the induced connection on the vector bundle? (EDIT: Yes.)

2. • CommentRowNumber2.
   • CommentAuthorhq932309
   • CommentTimeJul 7th 2019
   • (edited Jul 7th 2019)
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   Author: hq932309
   Format: MarkdownItexIn Definition 2.1, does there miss a pair of parenthesis in the first term in RHS of the equation? Is it better to show as $\nabla_{X_i} (\Phi (X_0, \dots, \hat{X_i}, \dots, X_p))$?

   In Definition 2.1, does there miss a pair of parenthesis in the first term in RHS of the equation? Is it better to show as $\nabla_{X_i} (\Phi (X_0, \dots, \hat{X_i}, \dots, X_p))$?