What question did this study set out to answer?

The primary aim is to classify different types of algebroids on the tangent and cotangent bundles of manifolds depending on closed 3-forms.

April 3, 2026Filomat0 citationsOpen Access

The exact Courant like algebroids

MDMiroslav DoupovecBrno University of Technology JKJan KurekMaria Curie-Skłodowska University WMWłodzimierz M. Mikulski

Key Points

The primary aim is to classify different types of algebroids on the tangent and cotangent bundles of manifolds depending on closed 3-forms.
Classified all types of algebroids including Courant, Lie, Leibniz, and dull algebroids.
Focused on manifolds with dimension m less than 3.
Analyzed the canonical dependence on closed 3-forms.
Identified specific structures of Courant, Lie, Leibniz, and dull algebroids on TM and T*M.
Demonstrated a connection between these algebroids and closed 3-forms on the manifold.

Abstract

Let M be an m-manifold. If m ? 3, we find all Courant algebroids, all Leibniz algebroids, all Lie algebroids and all dull algebroids on TM ? T* M canonically depending on closed 3-forms on M.

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