On scalar and total scalar curvatures of Riemann-Cartan manifolds
The Killing Tensors on an -dimensional Manifold with -structure
In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an -dimensional differentiable manifold endowed with an equiaffine -structure and discuss possible applications of obtained results in Riemannian geometry.
From infinitesimal harmonic transformations to Ricci solitons
The concept of the Ricci soliton was introduced by R. S. Hamilton. The Ricci soliton is defined by a vector field and it is a natural generalization of the Einstein metric. We have shown earlier that the vector field of the Ricci soliton is an infinitesimal harmonic transformation. In our paper, we survey Ricci solitons geometry as an application of the theory of infinitesimal harmonic transformations.
On Uniqueness Theoremsfor Ricci Tensor
In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold and a symmetric 2-tensor , construct a metric on whose Ricci tensor equals . In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with non-negative...
Page 1