Curvature of quaternionic skew-Hermitian manifolds and bundle constructions

Investor logo

Warning

This publication doesn't include Institute of Computer Science. It includes Faculty of Science. Official publication website can be found on muni.cz.
Authors

CHRYSIKOS Ioannis CORTES Vicente GREGOROVIČ Jan

Year of publication 2025
Type Article in Periodical
Magazine / Source Mathematische Nachrichten
MU Faculty or unit

Faculty of Science

Citation
web https://onlinelibrary.wiley.com/doi/10.1002/mana.202400301
Doi http://dx.doi.org/10.1002/mana.202400301
Keywords quaternionic structures; quaternionic skew-Hermitian structures; hypercomplex skew-Hermitian structures; bundle constructions
Description This paper is devoted to a description of the second-order differential geometry of torsion-free almost quaternionic skew-Hermitian manifolds, that is, of quaternionic skew-Hermitian manifolds (M, Q, \omega). We provide a curvature characterization of such integrable geometric structures, based on the holonomy theory of symplectic connections and we study qualitative properties of the induced Ricci tensor. Then, we proceed with bundle constructions over such a manifold (M, Q, \omega). In particular, we prove the existence of almost hypercomplex skew-Hermitian structures on the Swann bundle over M and investigate their integrability.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.

More info