Talk:Acceleration (differential geometry)

Use of abstract Index notation in FORMAL DEFINITION

I think that It is mixed the use of the abstract index notation and the local chart index notation, and that could be measleading. mantener refrigerado (talk) 07:30, 11 August 2019 (UTC)

No, it is not. Writing $\nabla _{\dot {\gamma }}{\dot {\gamma }}$, where $\nabla$ denotes the covariant derivative associated to $\Gamma$, is not using abstract index notation. Aurel.droud (talk) 08:49, 27 December 2019 (UTC)

Confusion of Differential Geometric Concepts in FORMAL DEFINITION

The article seems to have been written by physicists. At present, it does not meet the formal requirements and standards of mathematics.

In its section formal definition, the article mixes covariant derivatives of objects along a curve with covariant derivatives of objects in a spacetime. The article does not clarify, where "time" comes from, nor does it clarify how this notion of (spacetime) acceleration is related to the often used purely spatial acceleration. The same goes for spacetime velocity and spatial velocity.

Please be aware that the covariant derivative itself is defined for fields in the manifold itself (e.g. in spacetime). There is no parameter. This has to be distinguished from a covariant derivative along a curve, where there is a parameter. Nabla is the notation for the covariant derivative in the manifold.

Moreover, the last paragraph suddenly refers to unit vectors, but there was no metric provided. It is confusing insofar, as it does not say whether this notion of acceleration is defined for unit vectors only, in a (Pseudo-)Riemannian manifold, or whether this notion of acceleration is defined for general vector fields (along a curve). Up to renaming the objects and using different letters, the formula in the last paragraph is identical to the formula in the formal definition. This requires clarification.

In general, it seems that a proper context is missing: The article seems to have been written with a specific application (e.g. general relativity) in mind, with several implicit assumptions and conventions, which however are not shown in the article. Therefore, although the article might be clear to some very specific community of experts, it is not clear enough for a more general audience. EinMathematikerInAustria (talk) 08:51, 26 January 2025 (UTC)