Generalized almost even-Clifford manifolds and their twistor spaces

Abstract

Motivated by the recent interest in even-Clifford structures and in generalized complex and quaternionic geometries, we introduce the notion of generalized almost even-Clifford structure. We generalize the Arizmendi-Hadfield twistor space construction on even-Clifford manifolds to this setting and show that such a twistor space admits a generalized complex structure under certain conditions.

Keywords

• generalized complex structure
• even-clifford structure
• twistor space
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