New posts in tangent-bundle

Does every smooth local frame of the tangent bundle correspond to a chart?

differential-geometry smooth-manifolds vector-fields tangent-bundle

How to handle the differential of a vector field, ${\rm d}X:TM\to TTM$, in terms of (equivalence classes of) curves?

differential-geometry vector-bundles vector-fields differential tangent-bundle

Is there a canonical way of lifting a vector field $X$ on $M$ to its tangent bundle $TM$?

differential-geometry vector-fields classical-mechanics tangent-bundle

Why is the tangent bundle defined using a disjoint union?

differential-geometry differential-topology vector-bundles tangent-bundle tangent-spaces

What do the fibers of the double tangent bundle look like?

differential-geometry vector-bundles vector-fields tangent-bundle

Why is the Sasaki metric natural?

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Are $T\mathbb{S}^2$ and $\mathbb{S}^2 \times \mathbb{R}^2$ different?

differential-geometry algebraic-topology tangent-bundle

Why is the tangent bundle orientable?

differential-geometry smooth-manifolds vector-bundles fiber-bundles tangent-bundle