The Schouten-Van Kampen connection on the (1,1)-tensor bundle

Altunbas M., GEZER A.

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, cilt.67, sa.3, ss.557-567, 2018 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 67 Sayı: 3
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1007/s12215-018-0337-y
  • Dergi Adı: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.557-567
  • Anahtar Kelimeler: Schouten-Van Kampen connection, Riemannian metric, Tensor bundle
  • Atatürk Üniversitesi Adresli: Evet

Özet

The problems in the present paper are related to the Schouten-Van Kampen connection (del) over bar associated with the Levi-Civita connection (del) over tilde of the Riemannian metric g which includes both Sasaki and Cheeger-Gromoll type metrics on the (1, 1)-tensor bundle. Firstly, we define the Schouten-Van Kampen connection (del) over bar on the (1, 1)-tensor bundle and give some applications concerning (del) over bar. Secondly, we compute all forms of curvature tensors of Thirdly, we consider an almost product structure which is compatible with the Riemannian metric g and investigate the conditions under which this structure is parallel with respect to (del) over bar. Lastly, we define and study the deformation algebra of the connections ((del) over bar, (del) over tilde.).