We investigate brane world models in higher-derivative gravity theories where the gravitational Lagrangian is an arbitrary function of the Ricci scalar. Making use of the conformal equivalence of such gravity models and Einstein-Hilbert gravity with a scalar field, we deduce the main features of higher-derivative gravity brane worlds. We solve for a gravity model that has corrections quadratic ...

We determine the Killing spinors for a class of magnetic brane solutions with Minkowski worldvolume of the theory of AdS Einstein Maxwell theories in d dimensions. We also obtain curved magnetic brane solutions with Ricci-flat worldvolumes. If we demand that the curved brane solution admits Killing spinors, then its worldvolume must admit parallel spinors. Classes of Ricci-flat worldvolumes adm...

The object of the present paper is to investigate the applications of pseudo cyclic Ricci symmetric manifolds admitting a semi-symmetric metric connection to the general relativity and cosmology.

We prove the following results: (i) A Sasakian metric as a nontrivial Ricci soliton is null η-Einstein, and expanding. Such a characterization permits to identify the Sasakian metric on the Heisenberg group H as an explicit example of (non-trivial) Ricci soliton of such type. (ii) If an ηEinstein contact metric manifold M has a vector field V leaving the structure tensor and the scalar curvatur...

The Palatini gravitational action is enlarged by an arbitrary function $f(X)$ of the determinants Ricci tensor and metric, $X=|\textbf{det}.R|/|\textbf{det}.g|$. resulting Ricci-determinant theory exhibits novel deviations from general relativity. We study a particular realization where extension characterized square-root Ricci-determinant, $f(X)=\lambda_\text{Edd}\sqrt{X}$, which corresponds t...

Applying a well known result for attracting fixed points of biholomorphisms [4, 6], we observe that one immediately obtains the following result: if (Mn, g) is a complete non-compact gradient Kähler-Ricci soliton which is either steady with positive Ricci curvature so that the scalar curvature attains its maximum at some point, or expanding with non-negative Ricci curvature, then M is biholomor...

We establish the weak continuity of the Gauss-Coddazi-Ricci system for isometric embedding with respect to the uniform L-bounded solution sequence for p > 2, which implies that the weak limit of the isometric embeddings of the manifold is still an isometric embedding. More generally, we establish a compensated compactness framework for the Gauss-Codazzi-Ricci system in differential geometry. Th...

where r = ∫ Rdμ/ ∫ dμ is the average scalar curvature (R is the scalar curvature) and Ric is the Ricci curvature tensor of h. Hamilton then spectacularly illustrated the success of this method by proving, when n = 3, that if the initial Riemannian metric has strictly positive Ricci curvature it evolves through time to a positively curved Einstein metric h∞ on M . And, because n = 3, such a Riem...

‎The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds‎, ‎called‎, ‎super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [‎A.A‎. ‎Shaikh and A‎. ‎Patra‎, On a generalized class of recurrent manifolds‎, Arch‎. ‎Math‎. ‎(Brno) 46 (2010) 71--78‎.] and weakly generalized recurrent manifolds ...