Some integrability conditions for almost K\"ahler manifolds

Among other results, a compact almost K\"ahler manifold is proved to be K\"ahler if the Ricci tensor is semi-negative and its length coincides with that of the star Ricci tensor or if the Ricci tensor is semi-positive and its first order covariant derivatives are Hermitian. Moreover, it is shown that there are no compact almost K\"ahler manifolds with harmonic Weyl tensor and non-parallel semi-positive Ricci tensor. Stronger results are obtained in dimension 4.Comment: Latex2e, 13 page

Residual Strain Dependence on Matrix Structure in RHQ-Nb3Al Wires by Neutron Diffraction Measurement

We prepared three types of non-Cu RHQ-Nb3Al wire samples with different matrix structures: an all-Ta matrix,a composite matrix of Nb and Ta with a Ta inter filament, and an all-Nb matrix. Neutron diffraction patterns of the wire samples were measured at room temperature in J-PARC "TAKUMI". To obtain residual strains of materials, we estimated lattice constant a by multi-peak analysis in the wire. Powder sample of each wire was measured, where the powder was considered to be strain-free. The grain size of all the powder samples was below 0.02 mm. For wire sample with the all-Nb matrix, we also obtained lattice spacing d by a single-peak analysis. Residual strains of Nb3Al filament were estimated from the two analysis results and were compared. Result, residual strains obtained from the multi-peak analysis showed a good accuracy with small standard deviation. The multi-peak analysis results for the residual strains of Nb3Al filament in the three samples were all tensile residual strain in the axial direction, they are 0.12%, 0.12%, and 0.05% for the all-Ta matrix, the composite matrix, and the all-Nb matrix, respectively. Difference in the residual strain of Nb3Al filament between the composite and all-Nb matrix samples indicates that type of inter-filament materials show a great effect on the residual strain. In this paper, we report the method of measurement, method of analysis, and results for residual strain in the tree types of non-Cu RHO-Nb3Al wires.Comment: 7 pages, 8 figure