# Generalized Almost Product Structures and Generalized CRF-structures

## TL;DR

This paper characterizes orthogonal subbundles in generalized tangent bundles related to almost product structures, introduces a pure spinor formalism for generalized CRF-structures, and explores their deformations and local product decompositions.

## Contribution

It provides new characterizations of subbundles, develops a pure spinor formalism for generalized CRF-structures, and analyzes their deformations and local product structures.

## Key findings

- Characterization of orthogonal subbundles via B-field transforms
- Introduction of pure spinor formalism for generalized CRF-structures
- Analysis of infinitesimal deformations of generalized CRF-structures

## Abstract

We give several equivalent characterizations of orthogonal subbundles of the generalized tangent bundle defined, up to B-field transform, by almost product and local product structures. We also introduce a pure spinor formalism for generalized CRF-structure and investigate the resulting decomposition of the de Rham operator. As applications we give a characterization of generalized complex manifolds that are locally the product of generalized complex factors and discuss infinitesimal deformations of generalized CRF-structures.