Anonymous
6/10/2025, 10:55:21 PM
No.16694568
>>16694516
>Geometry is about distances and angles. i.e. metrics
According to whomst've? The voices in your head? So you're telling me that
>local coordinates and Jacobian transformations
>tangent and cotangent bundles
>tensor bundles
>principal and associated bundles (including frame bundles and tensor densities)
>connections and curvature forms
>Lie, exterior, and covariant derivatives
>volume forms, integration, and Stokes theorem
all have nothing to do with geometry and have no clear geometric interpretation? But when you suddenly introduce a metric (even though there is no canonical choice of metric on generic manifolds, it's completely fucking arbitrary), it's geometry? What do you get from it exactly?
>musical isomorphism
>distance and energy functionals
>Killing vector fields
>orthonormal frame bundles and spinor bundles
Geez, dude, sounds like a very boring and limited field of study, your "differential geometry". I'd stick with "differential topology" if you don't mind.
>Geometry is about distances and angles. i.e. metrics
According to whomst've? The voices in your head? So you're telling me that
>local coordinates and Jacobian transformations
>tangent and cotangent bundles
>tensor bundles
>principal and associated bundles (including frame bundles and tensor densities)
>connections and curvature forms
>Lie, exterior, and covariant derivatives
>volume forms, integration, and Stokes theorem
all have nothing to do with geometry and have no clear geometric interpretation? But when you suddenly introduce a metric (even though there is no canonical choice of metric on generic manifolds, it's completely fucking arbitrary), it's geometry? What do you get from it exactly?
>musical isomorphism
>distance and energy functionals
>Killing vector fields
>orthonormal frame bundles and spinor bundles
Geez, dude, sounds like a very boring and limited field of study, your "differential geometry". I'd stick with "differential topology" if you don't mind.