On tangent bundles of Walker four-manifolds

Abstract

The aim of this study is to explore the complete lifts of almost Norden structures on tangent bundles of Walker four-manifolds. Furthermore, we examine the integrability conditions of the complete lifts JC{J}^{C} of the proper almost complex structure and identify the conditions for the isotropic Kähler-Norden property of the structure JC{J}^{C} on (T(M4),JC,gC)\left(T\left({M}_{4}),{J}^{C},{g}^{C}). Finally, we investigate the holomorphic conditions of the Norden (Kähler-Norden) metrics gC{g}^{C} and discuss Quasi-Kähler-Norden metrics gC{g}^{C} on the tangent bundle (T(M4),φC,gC)\left(T\left({M}_{4}),{\varphi }^{C},{g}^{C}) of Walker four-manifolds.

Keywords

• norden metrics
• walker four-manifolds
• integrability conditions
• proper almost complex structure
• complete lifts
• symbolic computation
• 53b30
• 53c15
• 53c50