Quasi Einstein manifold is a simple and natural generalization of Einstein manifold. The object of the present paper is to study some properties of generalized quasi Einstein manifolds. We also discuss with space-matter tensor and some properties related to it. Two non-trivial examples have been constructed to prove the existence of generalized quasi Einstein spacetimes.
A regular normal parabolic geometry of type on a manifold gives rise to sequences of invariant differential operators, known as the curved version of the BGG resolution. These sequences are constructed from the normal covariant derivative on the corresponding tractor bundle , where is the normal Cartan connection. The first operator in the sequence is overdetermined and it is well known that yields the prolongation of this operator in the homogeneous case . Our first main result...
We consider a semisymmetric metric connection in an almost Kenmotsu manifold with its characteristic vector field belonging to the -nullity distribution and -nullity distribution respectively. We first obtain the expressions of the curvature tensor and Ricci tensor with respect to the semisymmetric metric connection in an almost Kenmotsu manifold with belonging to - and -nullity distribution respectively. Then we characterize an almost Kenmotsu manifold with belonging to -nullity distribution...
The object of the present paper is to study almost pseudo-Z-symmetric manifolds. Some geometric properties have been studied. Next we consider conformally flat almost pseudo-Z-symmetric manifolds. We obtain a sufficient condition for an almost pseudo-Z-symmetric manifold to be a quasi Einstein manifold. Also we prove that a totally umbilical hypersurface of a conformally flat () is a manifold of quasi constant curvature. Finally, we give an example to verify the result already obtained in Section...
Positioned eco-grammar systems (PEG systems, for short) were introduced in our previous papers. In this paper we engage in a new field of research, the hierarchy of PEG systems, namely in the hierarchy of the PEG systems according to the number of agents presented in the environment and according to the number of types of agents in the system.
We classify the isometries in the non-identity component of the whole isometry group of the symmetric space of positive 3 × 3 matrices of determinant 1: we determine the translation lengths, minimal spaces and fixed points at infinity.
In this paper we survey some recent results on rank one symmetric space.
We present curvature properties of pseudosymmetry type of some warped products of semi-Riemannian spaces of constant curvature.