The space of germs of extremal K\" ahler metrics in one dimension comprises three distinct R3{\Bbb R}^3 components

In the 1980s, Eugenio Calabi introduced the concept of {\it extremal K\" ahler metrics} as critical points of the $L^2$-norm functional of scalar curvature in the space of K\" ahler metrics belonging to a fixed K\"ahler class of a compact complex manifold $X$. Calabi demonstrated that extremal K\" ahler metrics always degenerate into Einstein metrics on compact Riemann surfaces. We define a K\"ahler metric $g$ on a domain of ${\Bbb C}^n$ as a {\it local extremal K\"ahler metric} of dimension $n$ if it satisfies the Euler-Lagrange equation of this functional, i.e. holomorphic is the $(1,0)$-part of the gradient vector field of the scalar curvature of $g$, in the domain. Our main result establishes that the space of all germs of local extremal, non-Einstein K\"ahler metrics of dimension one comprises three components, each diffeomorphic to ${\Bbb R}^3$.Comment: 14 pages. Yours comments are greatly appreciated

(E)-2-{3-[4-(Diphenyl­amino)styr­yl]-5,5-dimethyl­cyclo­hex-2-enyl­idene}­malono­nitrile

In the title compound, C31H27N3, the cyclo­hexene ring has an envelope configuration. In the crystal structure, there is an 34 Å3 void around the inversion center, but the low electron density (0.13 e Å−3) in the difference Fourier map suggests no solvent mol­ecule occupying this void. No hydrogen bonding is found in the crystal structure

2-Hydr­oxy-6,6-dimethyl­bicyclo­[3.1.1]heptane-2-carboxylic acid

The title compound, C10H16O3, with a bicyclo­[3.1.1]heptane unit, was obtained by oxidation of β-pinene. The asymmetric unit contains two independent mol­ecules with similar geometry: the six-membered rings in both mol­ecules adopt envelope conformations. In the crystal, the independent mol­ecules exist as O—H⋯O hydrogen-bonded dimers. The dimers are linked into helical chains along the b axis by O—H⋯O hydrogen bonds

THE INFLUENCE OF BACKPACK CARRIAGE ON TRUNK POSTURE IN CHILDREN DURING UNPLANNED GAIT TERMINATION

This study aimed to examine the trunk posture in children with different backpack loads during unplanned gait termination. Twelve school boys aged 9–10 years completed unplanned and planned gait termination with a backpack load of 0%, 10%, and 15% of their body weight (BW) while level walking. Trunk inclination angle and trunk range of motion at sagittal plane and spinal angle at frontal plane were examined. In comparison with 0% BW load condition, the spinal angle increased significantly at 10% and 15% BW load condition during gait termination (