We study integral curvature conditions for a Riemannian metric g on S4 that quantify the best bilipschitz constant between (S4,g) and standard S4. Our results show is controlled by L2-norm of Weyl tensor L1-norm Q-curvature, under those quantities are sufficiently small, has positive Yamabe Q-curvature mean-positive. The proof result achieved in two steps. Firstly, we construct quasiconformal m...

Commutative properties of four-dimensional generalized symmetric pseudo-Riemannian manifolds were considered. Specially, in this paper, we studied Skew-Tsankov and Jacobi-Tsankov conditions in 4-dimensional pseudo-Riemannian generalized symmetric manifolds.

In the first part of this paper, some theorems are given for a Riemannian manifold with semi-symmetric metric connection. In the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. We obtain some properties of this manifold having the vectors mentioned above.