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On Uniqueness Theoremsfor Ricci Tensor

Marina B. Khripunova, Sergey E. Stepanov, Irina I. Tsyganok, Josef Mikeš (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold M and a symmetric 2-tensor r , construct a metric on M whose Ricci tensor equals r . 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...

On Veronese-Borůvka spheres

Katsuei Kenmotsu (1997)

Archivum Mathematicum

In this paper, history of reserches for minimal immersions from constant Gaussian curvature 2-manifolds into space forms is explained with special emphasis of works of O. Borůvka. Then recent results for the corresponding probrem to classify minimal immersions of such surfaces in complex space forms are discussed.

On weakly cyclic Ricci symmetric manifolds

A. A. Shaikh, Sanjib Kumar Jana (2006)

Annales Polonici Mathematici

We introduce a type of non-flat Riemannian manifolds called weakly cyclic Ricci symmetric manifolds and study their geometric properties. The existence of such manifolds is shown by several non-trivial examples.

On Weakly W 3 -Symmetric Manifolds

Shyamal Kumar Hui (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The object of the present paper is to study weakly W 3 -symmetric manifolds and its decomposability with the existence of such notions. Among others it is shown that in a decomposable weakly W 3 -symmetric manifold both the decompositions are weakly Ricci symmetric.

On weakly φ -symmetric Kenmotsu Manifolds

Shyamal Kumar Hui (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The object of the present paper is to study weakly φ -symmetric and weakly φ -Ricci symmetric Kenmotsu manifolds. It is shown that weakly φ -symmetric and weakly φ -Ricci symmetric Kenmotsu manifolds are η -Einstein.

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