Vector fields which are biharmonic maps

Alem A., Kacimi B., ÖZKAN M.

JOURNAL OF GEOMETRY, cilt.113, sa.1, 2022 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 113 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s00022-022-00627-5
  • Dergi Adı: JOURNAL OF GEOMETRY
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Anahtar Kelimeler: Tangent bundle, Sasaki metric, Biharmonic maps, HARMONIC MAPPINGS, TANGENT BUNDLE, ENERGY
  • Gazi Üniversitesi Adresli: Evet

Özet

In this paper, an explicit expression of the bitension field of a vector field considered as a map from a Riemannian manifold (M, g) to its tangent bundle TM equipped with the Sasaki metric gs is provided. As a consequence, we show characterization theorem for a vector field to be biharmonic map. We prove non-existence results for left-invariant vector fields which are biharmonic without being harmonic maps and non-harmonic biharmonic maps respectively on uninaodular Lie groups of dimension three.