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Results tagged with vector-bundles
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user 156492
A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.
2
votes
Accepted
Riemannian vector bundle
Given a connection $A_{i\alpha}^\beta$ the curvature is
$$F_{ij\alpha}^\beta=\frac{\partial A_{j\alpha}^\beta}{\partial x^i}-\frac{\partial A_{i\alpha}^\beta}{\partial x^j}+A_{i\gamma}^\beta A_{j\alph …
- 2,247
2
votes
1
answer
180
views
Vector field along an immersion whose covariant derivative is the differential
Let $(M,g)$ be a Riemannnian manifold and let $f:\Sigma\to M$ be a smooth immersion. Then the vector bundle $f^\ast TM\to\Sigma$ has a natural bundle metric and metric-compatible connection. Can one c …
- 2,247