Horizontal Bundle
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, in the field of differential topology, given :E M, a smooth fiber bundle over a smooth manifold M, then the vertical bundle VE of E is the subbundle of the tangent bundle TE consisting of the vectors which are tangent to the fibers of E over M. A horizontal bundle is then a particular choice of a subbundle of TE which is complementary to VE, in other words provides a complementary subspace in each fiber. In full generality, the horizontal bundle concep...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, in the field of differential topology, given :E M, a smooth fiber bundle over a smooth manifold M, then the vertical bundle VE of E is the subbundle of the tangent bundle TE consisting of the vectors which are tangent to the fibers of E over M. A horizontal bundle is then a particular choice of a subbundle of TE which is complementary to VE, in other words provides a complementary subspace in each fiber. In full generality, the horizontal bundle concept is one way to formulate the notion of an Ehresmann connection on a fiber bundle. However, the concept is usually applied in more specific contexts.
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