Work

Curvature of quaternionic skew‐Hermitian manifolds and bundle constructions

Year: 2024

Type: article

Abstract: 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 . 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 . In particular, we prove the existence of almost hypercomplex skew‐Hermitian structures on the Swann bundle over M and investigate their integrability.

Source: Mathematische Nachrichten

DOI: 10.1002/mana.202400301

Authors: Ioannis Chrysikos, Vicente Cortés, Jan Gregorovič

Institutions: Masaryk University, Universität Hamburg, TU Wien, University of Ostrava

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,300

Funders: Deutsche Forschungsgemeinschaft, Grantová Agentura České Republiky, Austrian Science Fund