• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.417-423
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• 2006

The object of the present paper is to study a conformally flat quasi-Einstein space and its hypersurface.

• 대한수학회지
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• 제48권6호
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• pp.1327-1328
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• 2011

• Korean Journal of Mathematics
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• 제13권1호
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• pp.51-59
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• 2005

Let (M, $g$) be a compact oriented self-dual 4-dimensional Einstein manifold with positive sectional curvature. Then we show that, up to rescaling and isometry, (M, $g$) is $S^4$ or $\mathbb{C}\mathbb{P}_2$, with their cannonical metrics.

• 대한수학회보
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• 제54권3호
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• pp.967-973
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• 2017

We prove that a homogeneous square Einstein Finsler metric is either Riemannian or flat.

• 대한수학회보
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• 제60권3호
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• pp.705-715
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• 2023

In this paper, we present some new properties for p-biharmonic hypersurfaces in a Riemannian manifold. We also characterize the p-biharmonic submanifolds in an Einstein space. We construct a new example of proper p-biharmonic hypersurfaces. We present some open problems.

• 호남수학학술지
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• 제32권1호
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• pp.167-176
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• 2010

Let (B, $\check{g}$) and (N, $\hat{g}$) be Einstein manifolds. Then, we get a complete (necessary and sufficient) condition for the warped product manifold $B\;{\times}_f\;N\;:=\;(B\;{\times}\;N,\;\check{g}\;+\;f{\hat{g}}$) to be Einstein, and obtain a complete condition for the Einstein warped product manifold $B\;{\times}_f\;N$ to be weakly stable. Moreover, we get a complete condition for the map i : ($B,\;\check{g})\;{\times}\;(N,\;\hat{g})\;{\rightarrow}\;B\;{\times}_f\;N$, which is the identity map as a map, to be harmonic. Under the assumption that i is harmonic, we obtain a complete condition for $B\;{\times}_f\;N$ to be Einstein.

• 대한수학회보
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• 제50권5호
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• pp.1683-1691
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• 2013

In this paper, we obtain the criteria that the Riemannian manifold B is Einstein or a gradient Ricci soliton from the information of the second derivative of $f$ in the warped product space $R{\times}_fB$ with gradient Ricci solitons. Moreover, we construct new examples of non-Einstein gradient Ricci soliton spaces with an Einstein or non-Einstein gradient Ricci soliton leaf using our main theorems. Finally we also get analogous criteria for the Lorentzian version.

• Korean Journal of Mathematics
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• 제26권1호
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• pp.43-51
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• 2018

The manifold $^{\ast}g-ESX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^{\ast}g^{{\lambda}{\nu}}$ through the ES-connection which is both Einstein and semi-symmetric. The purpose of the present paper is to derive a new set of powerful recurrence relations and to prove a necessary and sufficient condition for a unique Einstein's connection to exist in 5-dimensional $^{\ast}g-ESX_5$ and to display a surveyable tnesorial representation of 5-dimensional Einstein's connection in terms of the unified field tensor, employing the powerful recurrence relations in the second class.

• 대한수학회보
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• 제56권5호
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• pp.1315-1325
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• 2019

The purpose of this article is to study the Ricci solitons and Ricci almost solitons on para-Kenmotsu manifold. First, we prove that if a para-Kenmotsu metric represents a Ricci soliton with the soliton vector field V is contact, then it is Einstein and the soliton is shrinking. Next, we prove that if a ${\eta}$-Einstein para-Kenmotsu metric represents a Ricci soliton, then it is Einstein with constant scalar curvature and the soliton is shrinking. Further, we prove that if a para-Kenmotsu metric represents a gradient Ricci almost soliton, then it is ${\eta}$-Einstein. This result is also hold for Ricci almost soliton if the potential vector field V is pointwise collinear with the Reeb vector field ${\xi}$.

• Journal of Korean Neurosurgical Society
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• 제63권6호
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• pp.777-783
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• 2020

Objective : To compare the accuracy and breach rates of freehand (FH) versus navigated (NV) pedicle screws in the thoracic and lumbar spine in patients with metastatic spinal tumors. Methods : A retrospective review of adult patients who underwent pedicle screw fixation in the thoracic or lumbar spine for metastatic spinal tumors between 2012 and 2018 was conducted. Breaches were assessed based on the Gertzbein and Robbins classification and only screws placed >4 mm outside of the pedicle wall (lateral or medial) were considered breached. Results : A total of 62 patients received 547 pedicle screws (average 8 per patient) - 34 patients received 298 pedicle screws in the FH group and 28 patients received 249 screws in the NV group. There were 40/547 breaches, corresponding to a breach and accuracy rate of 7.3% and 92.7%, respectively. The breach rate was 9.7% in the FH group and 4.4% in the NV group (chi-squared test, p=0.017); this corresponded to an accuracy rate of 90.3% and 95.6%, respectively. Only one patient from the overall cohort (in the FH group) required revision surgery due to a medial breach abutting the spinal cord (1.6% of all patients; 2.9% of FH patients); no patient suffered organ, vessel, or neurological injury from screw breaches. Conclusion : Navigated pedicle screw placement in patients with metastatic spinal tumors has a significantly higher radiographic accuracy compared to the FH technique. However, the revision surgery was low and no patient suffered from clinically-relevant breach. Navigation also offers the advantage of real-time localization of spinal tumors and aids in targeting and resection of these lesions.