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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

1 vote

Why do we use the less simple convention for the definition of a vector bundle connection?

The "usual" definition tantamounts to saying that $[\nabla, \omega ]=d\omega$, where $[,]$ is the (graded) commutator of (graded) endomorphisms.
Grimolatto's user avatar
4 votes
2 answers
541 views

Existence of connections making a bundle endomorphism parallel

Let $M$ be a manifold, $TM$ its tangent bundle, and $N:TM\to TM$ a vector bundle morphism. It is possible to find a torsionless linear connection $\nabla$ on $TM$ such that $\nabla N=0$?
Grimolatto's user avatar
0 votes
0 answers
69 views

Cohomology operators inducing local basis of $1-$forms

Suppose that $\partial$ is a non-trivial ($\partial \neq 0$) cohomology operator on an $m-$dimensional manifold $M$ (that is: $\partial:\Omega(M)\to\Omega(M)$ is a degree $1$ derivation such that $\pa …
Grimolatto's user avatar