Real hypersurfaces in complex two-plane Grassmannians with commuting restricted Jacobi operators

In this paper, we have considered a new commuting condition, that is, $(R_\xi\phi) S = S (R_\xi\phi)$ \big(resp. (\Bar{R}_N\phi) S = S (\Bar{R}_N\phi)\big) between the restricted Jacobi operator~$R_\xi\phi$ (resp. \Bar{R}_N\phi), and the Ricci tensor $S$ for real hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$. In terms of this condition we give a complete classification for Hopf hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$

Lie Derivatives and Ricci Tensor on Real Hypersurfaces in Complex Two-plane Grassmannians

On a real hypersurface M in a complex two-plane Grassmannian Gz(Cm+z) we have the Lie derivation L and a diòerential operator of order one associated with the generalized Tanaka– Webster connection L(k). We give a classiûcation of real hypersurfaces M on Gz(Cm+z) satisfying L (k) S = L S, where epsilon is the Reeb vector ûeld on M and S the Ricci tensor of M

Epidural cement leakage through pedicle violation after balloon kyphoplasty causing paraparesis in osteoporotic vertebral compression fractures - a report of two cases

Kyphoplasty is advantageous over vertebroplasty in terms of better kyphosis correction and diminished risk of cement extravasations. Literature described cement leakage causing neurological injury mainly after vertebroplasty procedure; only a few case reports show cement leakage with kyphoplasty without neurological injury or proper cause of leakage. We present a report two cases of osteoporotic vertebral compression fracture treated with kyphoplasty and developed cement leakage causing significant neurological injury. In both cases CT scan was the diagnostic tool to identify cause of cement leakage. CT scan exhibited violation of medial pedicle wall causing cement leakage in the spinal canal. Both patients displayed clinical improvement after decompression surgery with or without instrumentation. Retrospectively looking at stored fluoroscopic images, we found that improper position of trocar in AP and lateral view simultaneously while taking entry caused pedicle wall violation. We suggest not to cross medial pedicle wall in AP image throughout the entire procedure and keeping the trocar in the center of pedicle in lateral image would be the most important precaution to prevent such complication. Our case reports adds the neurological complications with kyphoplasty procedure and suggested that along with other precautions described in the literature, entry with trocar along the entire procedure keeping the oval shape of pedicle in mind (under C-arm) will probably help to prevent such complications