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Vol. 51 No. 1 (2025)
Serdica Mathematical Journal

Articles

On the type of generalized hypercomplex structures

https://doi.org/10.55630/serdica.2025.51.89-114

Published 14-10-2025

  • Anna Fino
    • ,
  • Gueo Grantcharov

Anna Fino
Università degli studi di Torino and Florida International University

Gueo Grantcharov
Florida International University

Abstract

The generalized hypercomplex structures defined within the framework of generalized geometry include hypercomplex and holomorphic symplectic structures as particular cases. They have a \(S^2\)-family of generalized complex structures, and in this paper we study the types of these structures and the corresponding twistor space. We show that there are generalized hypercomplex structures on the \(4n\)-dimensional tori, which do not contain a structure of maximal (complex) type.
Moreover, we show that the Kodaira-Thurston surface which has a holomorphic symplectic structure, admits also a generalized hypercomplex structure in which all generalized complex structures are of type 1.

2020 Mathematics Subject Classification:

53D18, 53C28

Keywords

generalized hypercomplex structure, twistor space

Full text

Author Details

Anna Fino

Dipartimento di Matematica “G. Peano”
Università degli studi di Torino
Via Carlo Alberto 10
10123 Torino, Italy
e-mail: annamaria.fino@unito.it
and
Department of Mathematics and Statistics
Florida International University
Miami, FL 33199, USA
e-mail: afino@fiu.edu

Gueo Grantcharov

Department of Mathematics and Statistics
Florida International University
Miami, FL 33199, USA
e-mail: grantchg@fiu.edu

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