Sasakian metric as a Ricci soliton and related results

We prove the following results: (i) A Sasakian metric as a non-trivial Ricci soliton is null $\eta$-Einstein, and expanding. Such a characterization permits to identify the Sasakian metric on the Heisenberg group $\mathcal{H}^{2n+1}$ as an explicit example of (non-trivial) Ricci soliton of such type. (ii) If an $\eta$-Einstein contact metric manifold $M$ has a vector field $V$ leaving the structure tensor and the scalar curvature invariant, then either $V$ is an infinitesimal automorphism, or $M$ is $D$-homothetically fixed $K$-contact.Comment: Non

Cosmological Models through Spatial Ricci Flow

We consider the synchronization of the Einstein’s flow with the Ricci-flow of the standard spatial slices of the Robertson–Walker space–time and show that associated perfect fluid solution has a quadratic equation of state and is either spherical and collapsing, or hyperbolic and expanding. Read More: http://www.worldscientific.com/doi/abs/10.1142/S021988781650069

Gradient Ricci Solitons with a Conformal Vector Field

We show that a connected gradient Ricci soliton (M,g,f,λ) with constant scalar curvature and admitting a non-homothetic conformal vector field V leaving the potential vector field invariant, is Einstein and the potential function f is constant. For locally conformally flat case and non-homothetic V we show without constant scalar curvature assumption, that f is constant and g has constant curvature

Some Results on Almost Ricci Solitons and Geodesic Vector Fields.

We show that a compact almost Ricci soliton whose soliton vector field is divergence-free is Einstein and its soliton vector field is Killing. Next we show that an almost Ricci soliton reduces to Ricci soliton if and only if the associated vector field is geodesic. Finally, we prove that a contact metric manifold is K-contact if and only if its Reeb vector field is geodesic

Almost Ricci Solitons and K-Contact Geometry

We give a short Lie-derivative theoretic proof of the following recent result of Barros et al. “A compact non-trivial almost Ricci soliton with constant scalar curvature is gradient, and isometric to a Euclidean sphere”. Next, we obtain the result: a complete almost Ricci soliton whose metric g is K-contact and flow vector field X is contact, becomes a Ricci soliton with constant scalar curvature. In particular, for X strict, g becomes compact Sasakian Einstein

Book Review of Teaching and Learning with Technology: Pushing boundaries and breaking down walls

Book review of Teaching and Learning with Technology: Pushing boundaries and breaking down walls, edited by Som Naidu and Sharishna Narayan and published in 2020 by The University of the South Pacific Press

The impact of the WTO agricultural negotiating modalities on Southern African Development Community countries

This paper assesses the likely impact on the agricultural sector of the Southern African Development Community (SADC) countries of the Harbinson modalities, along with the EU and US proposals as alternative scenarios in the context of the ongoing negotiations of the WTO Agreement on Agriculture. Impacts are assessed on a number of indicators, notably government revenue, producer, consumer and total welfare measures and trade flow. Reflecting country- and commodity-specific factors, the three modalities have different impacts on the indicators. The SADC as a whole is found to lose in terms of total welfare under all three proposals. But while this loss under the Harbinson and EU proposals is due to declines in consumer surpluses and government revenues, reduced producer surplus and government revenue explain the loss in total welfare under the US proposal. Thus, the ranking of the modalities differs according to the impact indicator used, revealing important trade-offs in the choice of the modalities. An issue raised is the value of consumer gains relative to producer gains for low-income economies highly dependent on agriculture because for them effective demand for consumption itself depends on incomes generated from increased agricultural activities, which in turn requires sustained gains in producer surpluses. The paper presents a range of results and discusses the trade-offs, with the hope that SADC trade negotiators and policy makers find these to be useful as they negotiate for the final form of the modalities.International Relations/Trade,