Andreas Cap, Jan Slovak
On Local Flatness of Manifolds with AHS-Structures
The paper is published: Supp. ai Rend. Circolo Matematico di Palermo, Ser. II, 43 (1996) 95-101

MSC:

53C10 $G$-structures

53C05 Connections, general theory

Abstract: The AHS--structures on manifolds are the simplest cases of the so called
parabolic geometries which are modeled on homogeneous spaces corresponding
to a parabolic subgroup in a semisimple Lie group. It covers the cases
where the
negative parts of the graded Lie algebras in question are abelian. In the
series \cite{\v Cap, Slov\'ak, Sou\v cek, 94, 95}, the authors developed a
consistent frame bundle approach to the subject. Here we give explicit
descriptions of the obstructions against the flatness of such structures
based on the latter approach. In particular we recover the
results proved in \cite{Baston} for complex manifolds in the real smooth
setting.

Keywords: almost Hermitian symmetric structure, AHS-structure, locally flat, Cartan connection