It is shown that a class of 4-dimensional Lorentzian framed space-times (defined by a linear operator satisfying certain algebraic and geometric conditions) admitting a nonsingular simple electromagnetic field possesses a two parameter abelian group of affine conformal motions. Based on this, we have studied the problem of finding various types of inheriting electromagnetic field plus perfect fluid solutions. A sub-class of such spaces exists whose geometry is conformal to a physical space-time having an invertible two parameter abelian isometry group. Thus, our work is related to the Carter's theorems on Killing Horizons.

https://link.springer.com/content/pdf/10.1007%2FBF01762387.pdf

Integral formulas in riemannian geometry

Some applications of globally framed structures to relativity

Some characterizations of property of trans-Sasakian 3-manifolds

There are several generalizations of the concept of semi-symmetric Riemannian manifolds. In the present paper, we consider some special types of generalized semi-symmetric Riemannian manifolds with positive or negative defined curvature operator or sectional curvature. As applications of our theory we prove some propositions about semi-symmetric, Ricci-semi-symmetric and birecurrent Riemannian manifolds.

https://cab.unime.it/journals/index.php/AAPP/article/download/AAPP.91S2A1/AAPP91S2A1

On generalized semisymmetric Riemannian manifolds

Let (M;g) be a compact Riemannian manifold of dimension n. The aim of the present paper is to study the dimension of K q (M;R) in the connection with the Riemannian metric g on M.

http://www.mathem.pub.ro/bjga/v01n1/B01-1-TS.PDF

On the Killing Tensor Fields on a Compact Riemannian Manifold

In the paper, we study evolution equations of the scalar and Ricci curvatures under the Hamilton’s Ricci flow on a closed manifold and on a complete noncompact manifold. In particular, we study conditions when the Ricci flow is trivial and the Ricci soliton is Ricci flat or Einstein.

Integral formulas in riemannian geometry

Citations

Some applications of globally framed structures to relativity

Some characterizations of property of trans-Sasakian 3-manifolds

On generalized semisymmetric Riemannian manifolds

On the Killing Tensor Fields on a Compact Riemannian Manifold

On Evolution Equations Under the Hamilton’s Ricci Flow

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