On a class of N(k)-mixed generalized quasi-Einstein manifolds

The objective of the present paper is to study N(k)-mixed generalized quasi-Einstein manifolds. We prove the existence of these manifolds. Later we establish some curvature properties of N(k)-mixed generalized quasi-Einstein manifolds under certain conditions. In the last section, we give two examples of N(k)-mixed generalized quasi-Einstein manifolds

On φ-pseudo symmetric LP-Sasakian manifolds with respect to quarter-symmetric non-metric connections

The object of the present paper is to study φ-pseudo symmetric and φ-pseudo Ricci symmetric LP-Sasakian manifolds with respect to Levi–Civita connections and quarter-symmetric non-metric connections. We obtain a necessary and sufficient condition for a φ-pseudo symmetric LP-Sasakian manifold with respect to a quarter symmetric non-metric connection to be φ-pseudo symmetric LP-Sasakian manifold with respect to a Levi–Civita connection

Conformal mappings of mixed generalized quasi-Einstein manifolds admitting special vector fields

It is known that Einstein manifolds form a natural subclass of the class of quasi-Einstein manifolds and plays an important role in geometry as well as in general theory of relativity. In this work, we investigate conformal mapping of mixed generalized quasi- Einstein manifolds, considering a conformal mapping between two mixed generalized quasi- Einstein manifolds Vn and V ̅n. We also find some properties of this transformation from Vn to V ̅n and some theorems are proved. Considering this mapping, we peruse some properties of these manifolds. Later, we also study some special vector fields under these mapping on this manifolds and some theorems about them are proved.Gobierno de la India. Primer autor apoyado por DST / INSPIRE Fellowship / 2013/1041peerReviewe

Differential regional expression patterns of alpha-synuclein, TNF-alpha, and IL-1beta; and variable status of dopaminergic neurotoxicity in mouse brain after Paraquat treatment

BACKGROUND: Paraquat (1, 1-dimethyl-4, 4-bipyridium dichloride; PQ) causes neurotoxicity, especially dopaminergic neurotoxicity, and is a supposed risk factor for Parkinson's disease (PD). However, the cellular and molecular mechanisms of PQ-induced neurodegeneration are far from clear. Previous studies have shown that PQ induces neuroinflammation and dopaminergic cell loss, but the prime cause of those events is still in debate. METHODS: We examined the neuropathological effects of PQ not only in substantia nigra (SN) but also in frontal cortex (FC) and hippocampus of the progressive mouse (adult Swiss albino) model of PD-like neurodegeneration, using immunohistochemistry, western blots, and histological and biochemical analyses. RESULTS: PQ caused differential patterns of changes in cellular morphology and expression of proteins related to PD and neuroinflammation in the three regions examined (SN, FC and hippocampus). Coincident with behavioral impairment and brain-specific ROS generation, there was differential immunolocalization and decreased expression levels of tyrosine hydroxylase (TH) in the three regions, whereas α-synuclein immunopositivity increased in hippocampus, increased in FC and decreased in SN. PQ-induced neuroinflammation was characterized by area-specific changes in localization and appearances of microglial cells with or without activation and increment in expression patterns of tumor necrosis factor-α in the three regions of mouse brain. Expression of interleukin-1β was increased in FC and hippocampus but not significantly changed in SN. CONCLUSION: The present study demonstrates that PQ induces ROS production and differential α-synuclein expression that promotes neuroinflammation in microglia-dependent or -independent manners, and produces different patterns of dopaminergic neurotoxicity in three different regions of mouse brain