Definition:Smooth Fiber Metric
Jump to navigation
Jump to search
Definition
Let $E \to M$ be a smooth vector bundle.
Let $p \in E$.
Let $E_p$ be a fiber at $p$.
Let $\sigma, \tau$ be smooth sections of $E$.
Suppose on each $E_p$ the inner product $\innerprod \sigma \tau$ is a smooth function.
Then the inner product $\innerprod \cdot \cdot$ is called the smooth fiber metric (on $E$).
![]() | This article needs to be linked to other articles. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by adding these links. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{MissingLinks}} from the code. |
![]() | Further research is required in order to fill out the details. In particular: Fibers, bundles You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by finding out more. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Research}} from the code. |
Sources
- 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 2$: Riemannian Metrics. Basic Constructions on Riemannian Manifolds