An Abstract Morimoto Theorem for Generalized $F$-structures

TL;DR

This paper generalizes Morimoto's theorem to generalized $F$-structures, providing new insights into complex structures on product manifolds and extending classical results to broader geometric contexts.

Contribution

It introduces an abstract Morimoto theorem for generalized $F$-structures, extending complex structure constructions beyond global product manifolds.

Findings

Characterizes invariant generalized complex structures on product manifolds with Lie group factors

Generalizes a theorem on Hermitian bicontact manifolds

Provides a new framework for complex structures on non-product manifolds

Abstract

We abstract Morimoto's construction of complex structures on product manifolds to pairs of certain generalized $F$-structures on manifolds that are not necessarily global products. As applications we characterize invariant generalized complex structures on product manifolds in which one factor is a Lie group and we generalize a theorem of Blair, Ludden and Yano on Hermitian bicontact manifolds.