Let M be a real hypersurface of a complex space form M n (c), c = 0, and suppose that the structure vector field ξ is an eigen vector field of the Ricci tensor S, which satisfies Sξ = βξ where β is a function. We show that if (∇ X S)Y is proportional to ξ for any vector fields X and Y orthogonal to ξ , then M is a Hopf hypersurface, and if it is perpendicular to ξ , then M is a ruled real hypersurface.

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Neuroeconomics has the potential to fundamentally change the way economics is done. This article identifies the ways in which this will occur, pitfalls of this approach, and areas where progress has already been made. The value of neuroeconomics studies for social policy lies in the quality, replicability, and relevance of the research produced. While most economists will not contribute to the neuroeconomics literature, we contend that most economists should be reading these studies.

We show that there is no proper CR submanifold with semi-flat normal connection and semi-parallel second fundamental form in a complex space form with nonzero constant holomorphic sectional curvature such that the dimension of the holomorphic tangent space is greater than 2.

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