K\"{a}hler-Norden structures on Hom-Lie groups and Hom-Lie algebras

Yıl 2024, Erken Görünüm, 1 - 24

E. Peyghan Leila Nourmohammadifar Abdenacer Makhlouf Aydın Gezer

https://doi.org/10.15672/hujms.1344687

Öz

The aim of this paper is to describe two geometric notions, holomorphic Norden structures and K\"{a}hler-Norden structures on Hom-Lie groups, and study their relationships in the left invariant setting. We study K\"{a}hler-Norden structures with abelian complex structures and give the curvature properties of holomorphic Norden structures on Hom-Lie groups. Finally, we show that any left-invariant holomorphic Hom-Lie group is a flat (holomorphic Norden Hom-Lie algebra carries a Hom-Left-symmetric algebra) if its left-invariant complex structure (complex structure) is abelian.

Anahtar Kelimeler

Hom-Lie group, Hom-Lie algebra, holomorphic Norden structure, K\"{a}hler-Norden structure

Kaynakça

• [1] A. Borowiec, M. Ferraris, M. Francaviglia and I. Volovich, Almost-complex and almost-product Einstein manifolds from a variational principle, J. Math. Phys. 40 (7), 3446–3464, 1999.