We consider a bi-invariant Lie group (G, g) and we equip its tangent bundle TG with the left invariant Riemannian metric introduced in the paper of Asgari and Salimi Moghaddam. We investigate Einstein-like, Ricci soliton, and Yamabe soliton structures on TG. Then we study some geometrical tensors on TG such as Cotton, Schouten, Weyl, and Bach tensors, and we also compute projective and concircular and m-projective curvatures on TG. Finally, we compute the Szabo operator and Jacobi operator on the tangent Lie group TG.
Cotton tensor, Einstein-like structure, Lie group, soliton structure, Schouten tensor, Yamabe soliton
SEIFIPOUR, DAVOOD and PEYGHAN, ESMAEIL
"Some properties of Riemannian geometry of the tangent bundle of Lie groups,"
Turkish Journal of Mathematics: Vol. 43:
6, Article 16.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss6/16