The mirror map and other natural tangent tensors

TL;DR

This paper reviews the intrinsic geometry of the tangent bundle of a manifold, focusing on the mirror map and tangent tensors, addressing cohomological questions and properties of the canonical endomorphism.

Contribution

It provides a comprehensive review of the mirror map and tangent tensors, including new insights into their cohomological properties and induced operators.

Findings

Analysis of the mirror map's properties

Solutions to cohomological questions related to tangent tensors

Insights into the structure of the tangent bundle

Abstract

We review the intrinsic geometry of the tangent bundle of a differentiable manifold $M$, aside from any non-natural structures. We recall the properties of the mirror map $B\in\mathrm{End}(TTM)$, known also as the canonical endomorphism or the almost-tangent structure, solve some cohomological questions and raise other induced by the $\mathrm{d}_B$ operator.