Norden structures on cotangent bundles

TL;DR

This paper explores how Norden structures on manifolds extend to their cotangent bundles, demonstrating that certain geometric properties are preserved or enhanced in the cotangent bundle context.

Contribution

It proves that cotangent bundles of complex Norden manifolds inherit Norden structures, and establishes conditions under which these structures are integrable or Kähler Norden flat.

Findings

Cotangent bundle of a complex Norden manifold admits a Norden structure.

If the original manifold has a flat natural connection, the cotangent bundle's structure is integrable.

Kähler Norden flatness is preserved in the cotangent bundle under certain conditions.

Abstract

We study prolongation of Norden structures on manifolds to their generalized tangent bundles and to their cotangent bundles. In particular, by using methods of generalized geometry, we prove that the cotangent bundle of a complex Norden manifold $(M,J,g)$ admits a structure of Norden manifold, $(T^{\star}(M),\tilde J, \tilde g)$. Moreover if $(M,J,g)$ has flat natural canonical connection then $\tilde J$ is integrable, that is $(T^{\star}(M),\tilde J, \tilde g)$ is a complex Norden manifold. Finally we prove that if $(M,J,g)$ is K\"ahler Norden flat then $(T^{\star}(M),\tilde J, \tilde g)$ is K\"ahler Norden flat.