Some Notes on Metallic Kahler Manifolds

GEZER A., Topcuoglu F., De U. C.

FILOMAT, cilt.35, sa.6, ss.1963-1975, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 6
  • Basım Tarihi: 2021
  • Doi Numarası: 10.2298/fil2106963g
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Sayfa Sayıları: ss.1963-1975
  • Anahtar Kelimeler: Conformal recurrency, conformal transformation, metallic Kahler manifold, hybrid tensor, Z-form
  • Atatürk Üniversitesi Adresli: Evet

Özet

The present paper deals with metallic Kahler manifolds. Firstly, we define a tensor H which can be written in terms of the (0, 4)-Riemannian curvature tensor and the fundamental 2-form of a metallic Kahler manifold and study its properties and some hybrid tensors. Secondly, we obtain the conditions under which a metallic Hermitian manifold is conformal to a metallic Kahler manifold. Thirdly, we prove that the conformal recurrency of a metallic Kahler manifold implies its recurrency and also obtain the Riemannian curvature tensor form of a conformally recurrent metallic Kahler manifold with non-zero scalar curvature. Finally, we present a result related to the notion of Z recurrent form on a metallic Kahler manifold.