On the projective Ricci curvature

The notion of the Ricci curvature is defined for sprays on a manifold. With a volume form on a manifold, every spray can be deformed to a projective spray. The Ricci curvature of a projective spray is called the projective Ricci curvature. In this paper, we introduce the notion of projectively Ricci-flat sprays. We establish a global rigidity result for projectively Ricci-flat sprays with nonnegative Ricci curvature. Then we study and characterize projectively Ricci-flat Randers metrics

Correlation between intercalated magnetic layers and superconductivity in pressurized EuFe2(As0.81P0.19)2

We report comprehensive high pressure studies on correlation between intercalated magnetic layers and superconductivity in EuFe2(As0.81P0.19)2 single crystal through in-situ high pressure resistance, specific heat, X-ray diffraction and X-ray absorption measurements. We find that an unconfirmed magnetic order of the intercalated layers coexists with superconductivity in a narrow pressure range 0-0.5GPa, and then it converts to a ferromagnetic (FM) order at pressure above 0.5 GPa, where its superconductivity is absent. The obtained temperature-pressure phase diagram clearly demonstrates that the unconfirmed magnetic order can emerge from the superconducting state. In stark contrast, the superconductivity cannot develop from the FM state that is evolved from the unconfirmed magnetic state. High pressure X-ray absorption (XAS) measurements reveal that the pressure-induced enhancement of Eu's mean valence plays an important role in suppressing the superconductivity and tuning the transition from the unconfirmed magnetic state to a FM state. The unusual interplay among valence state of Eu ions, magnetism and superconductivity under pressure may shed new light on understanding the role of the intercalated magnetic layers in Fe-based superconductors