On the special Finsler metric

Nany Lee 대한수학회 2003 대한수학회보 Vol.40 No.3

Given a Riemannian manifold (M,alpha ) with an almost Hermitianstructure f and a non-vanishing covariant vector field b,,consider the generalized Randers metric L=alpha +beta ,,where beta is a special singular Riemannian metric defined byb and f. This metric L is called an (a,b,f)-metric. Wecompute the inverse and the determinant of the fundamental tensor(g_{ij}) of an (a,b,f)-metric. Then we determine the maximaldomain mathcal{D}, of TMsetminus O, for an(a,b,f)-manifold where a y-local Finsler structure L, isdefined. And then we show that any (a,b,f)-manifold isquasi-C-reducible and find a condition under which an(a,b,f)-manifold is C-reducible.

ON THE GENERALIZED RANDERS CHANGE OF BERWALD METRICS

Lee, Nany The Kangwon-Kyungki Mathematical Society 2010 한국수학논문집 Vol.18 No.4

In this paper, we study the generalized Randers change $^*L(x,y)=L(x,y)+b_i(x,y)y^i$ from the Brewald metric L and the h-vector $b_i$. And in search for a non-Berwald Landsberg metric, we obtain the conditions on $b_i(x,y)$ under which $^*L$ is a Landsberg metric.

LICHNEROWICZ CONNECTIONS IN ALMOST COMPLEX FINSLER MANIFOLDS

LEE, NANY,WON, DAE-YEON Korean Mathematical Society 2005 대한수학회보 Vol.42 No.2

We consider the connections $\nabla$ on the Rizza manifold (M, J, L) satisfying ${\nabla}G=0\;and\;{\nabla}J=0$. Among them, we derive a Lichnerowicz connection from the Cart an connection and characterize it in terms of torsion. Generalizing Kahler condition in Hermitian geometry, we define a Kahler condition for Rizza manifolds. For such manifolds, we show that the Cartan connection and the Lichnerowicz connection coincide and that the almost complex structure J is integrable.

ZERMELO'S NAVIGATION PROBLEM ON HERMITIAN MANIFOLDS

Lee, Nany The Kangwon-Kyungki Mathematical Society 2006 한국수학논문집 Vol.14 No.1

In this paper, we apply Zermelo's problem of navigation on Riemannian manifolds to Hermitian manifolds. Using a similar technique with which we define a Randers metric in a Finsler manifold by perturbing Riemannian metric with a vector field, we construct an $(a,b,f)$-metric in a Rizza manifold from a Hermitian metric and a given vector field.

ON AN APPLICATION OF EXTERIOR DIFFERENTIAL SYSTEM TO FINSLER GEOMETRY

LEE,NANY 서울市立大學校 1998 論文集 Vol.32 No.1

이 논문에서는 E. Cartan의 외미분계를 휜슬러 기하의 등거리 묻기로 응용하였다. 외미분계를 휜슬러 기하의 입장에서 다시 해석하였다. Cartan-Janet의 정리를 작접 응용하여 어떤 곡률에 대한 가정 아래 휜슬러 다양체를 국소적으로 유클리드 공간으로 등거리로 묻을 수 있음을 보였다. In this paper, we apply the theory of exterior differential system of E. Cartan to the isometric embedding of Finsler manifolds into a Euclidean space. We rephrase the theory of exterior differential system under the setting of Finsler geometry. As a direct application of Cartan-Janet theorem, we show that a Finsler manifold can be locally isometrically embedded into a certain Euclidean space under the assumptions on the mixed and vertical curvatures.

ISOMETRIC IMMERSIONS OF FINSLER MANIFOLDS

Lee, Nany,Won, Dae Yeon The Kangwon-Kyungki Mathematical Society 2009 한국수학논문집 Vol.17 No.1

For an isometric immersion $f:M{\rightarrow}{\bar{M}}$ of Finsler manifolds M into $\bar{M}$, we compare the intrinsic Chern connection on M and the induced connection on M: We find the conditions for them to coincide and generalize the equations of Gauss, Ricci and Codazzi to Finsler submanifolds. In case the ambient space is a locally Minkowskian Finsler manifold, we simplify the above equations.

A retrospective analysis of etiology and outcomes of hemophagocytic lymphohistiocytosis in children and adults

( Abraham Kwak ),( Nani Jung ),( Ye Jee Shim ),( Heung Sik Kim ),( Hyun Ji Lim ),( Jae Min Lee ),( Mi Hwa Heo ),( Young Rok Do ) 영남대학교 의과대학 2021 Yeungnam University Journal of Medicine Vol.38 No.3

Background: Hemophagocytic lymphohistiocytosis (HLH) is a rare but severe, life-threatening inflammatory condition if untreated. We aimed to investigate the etiologies, outcomes, and risk factors for death in children and adults with HLH. Methods: The medical records of patients who met the HLH criteria of two regional university hospitals in Korea between January 2001 and December 2019 were retrospectively investigated. Results: Sixty patients with HLH (35 children and 25 adults) were included. The median age at diagnosis was 7.0 years (range, 0.1-83 years), and the median follow-up duration was 8.5 months (range, 0-204 months). Four patients had primary HLH, 48 patients had secondary HLH (20 infection-associated, 18 neoplasm-associated, and 10 autoimmune-associated HLH), and eight patients had HLH of unknown cause. Infection was the most common cause in children (14/35, 40.0%), whereas neoplasia was the most common cause in adults (13/25, 52.0%). Twenty-eight patients were treated with HLH-2004/94 immunochemotherapy. The 5-year overall survival (OS) rate for all HLH patients was 59.9%. The 5-year OS rates for patients with primary, infection-associated, neoplasm-associated, autoimmune-associated, and unknown cause HLH were 25.0%, 85.0%, 26.7%, 87.5%, and 62.5%, respectively. Using multivariate analysis, neoplasm-induced HLH (p=0.001) and a platelet count <50×10⁹/L (p=0.008) were identified as independent risk factors for poor prognosis in patients with HLH. Conclusion: Infection was the most common cause of HLH in children, while it was neoplasia in adults. The 5-year OS rate for all HLH patients was 59.9%. HLH caused by an underlying neoplasm or a low platelet count at the time of diagnosis were risk factors for poor prognosis.

Short stature and growth hormone deficiency in a girl with encephalocraniocutaneous lipomatosis and Jaffe-Campanacci syndrome: a case report

Eun Mi Choi,Nani Jung,심예지,최희정,Joon Sik Kim,Heung Sik Kim,송광순,Hee Jung Lee,김상표 대한소아내분비학회 2016 Annals of Pediatirc Endocrinology & Metabolism Vol.21 No.4

A 9-year-old Tajikistani girl presented to Keimyung University Dongsan Medical Center for evaluation of a skin lesion on her left eyelid, focal alopecia, unilateral ventricular dilatation, and aortic coarctation. She was diagnosed with encephalocraniocutaneous lipomatosis (ECCL) according to Moog’s diagnostic criteria. Café-au-lait spots were found on the left side of her trunk. Multiple nonossifying fibromas were found on her left proximal humerus, left distal femur, both proximal tibias, and left proximal fibula, suggesting Jaffe-Campanacci syndrome (JCS), following imaging of the extremities. Many JCS cases with multiple Café-au-lait macules, multiple nonossifying fibromas may actually have Neurofibromatosis type-1 (NF1). Thus, comprehensive molecular analysis to exclude NF1 mutation was performed using her blood sample. The NF1 mutation was not found. Her height was under the 3rd percentile and her bone age was delayed as compared with her chronological age. Baseline growth hormone (GH) level was below the normal range. Using the insulin stimulation and levodihydroxyphenylalanine tests, GH deficiency was confirmed. We present a case of GH deficiency with typical features of ECCL and JCS.

CONNECTIONS ON ALMOST COMPLEX FINSLER MANIFOLDS AND KOBAYASHI HYPERBOLICITY

Won, Dae-Yeon,Lee, Nany Korean Mathematical Society 2007 대한수학회지 Vol.44 No.1

In this paper, we establish a necessary condition in terms of curvature for the Kobayashi hyperbolicity of a class of almost complex Finsler manifolds. For an almost complex Finsler manifold with the condition (R), so-called Rizza manifold, we show that there exists a unique connection compatible with the metric and the almost complex structure which has the horizontal torsion in a special form. With this connection, we define a holomorphic sectional curvature. Then we show that this holomorphic sectional curvature of an almost complex submanifold is not greater than that of the ambient manifold. This fact, in turn, implies that a Rizza manifold is hyperbolic if its holomorphic sectional curvature is bounded above by -1.

Survival and Prognosis of Patients with Pilocytic Astrocytoma: A Single-Center Study

( Jae Hui Park ),( Nani Jung ),( Seok Jin Kang ),( Heung Sik Kim ),( El Kim ),( Hee Jung Lee ),( Hye Ra Jung ),( Misun Choe ),( Ye Jee Shim ) 대한뇌종양학회·대한신경종양학회·대한소아뇌종양학회 2019 Brain Tumor Research and Treatment Vol.7 No.2

Background Pilocytic astrocytoma (PA) is a brain tumor that is relatively more common in children and young adults. Methods We retrospectively reviewed the medical records of patients with PA treated at a single center between 1988 and 2018. Results We included 31 subjects with PA. The median age at diagnosis was 13.4 years, and the median follow-up duration was 9.9 years. The total PA group had a 10-year disease-specific survival (DSS) rate of 92.6% [95% confidence interval (CI), 82.6-100] and 10-year progression-free survival (PFS) rate of 52.8% (95% CI, 32.0-73.6). In patients aged <20 years, tumors were more likely to be located in sites in which gross total tumor resection (GTR) was impossible. No statistically significant difference in 10-year DSS was found between the GTR (100%) and non-GTR (89.7%; 95% CI, 76.2-100; p=0.374) groups. However, a statistically significant difference in 10-year PFS was found between the GTR (100%) and non-GTR groups (30.7%; 95% CI, 8.6-52.8; p=0.012). In the non-GTR group, no statistically significant difference in 10-year DSS was found between the patients who received immediate additional chemotherapy and/or radiotherapy (Add-Tx group, 92.9%; 95% CI, 79.4-100) and the non-Add-Tx group (83.3%; 95% CI, 53.5-100; p=0.577). No statistically significant difference in 10- year PFS was found between the Add-Tx group (28.9%; 95% CI, 1.7-56.1) and non-Add-Tx group (33.3%; 95% CI, 0-70.9; p=0.706). Conclusion The PFS of the patients with PA in our study depended only on the degree of surgical excision associated with tumor location. This study is limited by its small number of patients and retrospective nature. A multicenter and prospective study is necessary to confirm these findings.