Real hypersurfaces with Miao-Tam critical metrics of complex space forms

Xiaomin Chen 대한수학회 2018 대한수학회지 Vol.55 No.3

Let $M$ be a real hypersurface of a complex space form with constant curvature $c$. In this paper, we study the hypersurface $M$ admitting Miao-Tam critical metric, i.e., the induced metric $g$ on $M$ satisfies the equation: $-(\Delta_g\lambda)g+\nabla^2_g\lambda-\lambda Ric=g$, where $\lambda$ is a smooth function on $M$. At first, for the case where $M$ is Hopf, $c=0$ and $c\neq0$ are considered respectively. For the non-Hopf case, we prove that the ruled real hypersurfaces of non-flat complex space forms do not admit Miao-Tam critical metrics. Finally, it is proved that a compact hypersurface of a complex Euclidean space admitting Miao-Tam critical metric with $\lambda>0$ or $\lambda<0$ is a sphere and a compact hypersurface of a non-flat complex space form does not exist such a critical metric.

REAL HYPERSURFACES WITH MIAO-TAM CRITICAL METRICS OF COMPLEX SPACE FORMS

Chen, Xiaomin Korean Mathematical Society 2018 대한수학회지 Vol.55 No.3

Let M be a real hypersurface of a complex space form with constant curvature c. In this paper, we study the hypersurface M admitting Miao-Tam critical metric, i.e., the induced metric g on M satisfies the equation: $-({\Delta}_g{\lambda})g+{\nabla}^2_g{\lambda}-{\lambda}Ric=g$, where ${\lambda}$ is a smooth function on M. At first, for the case where M is Hopf, c = 0 and $c{\neq}0$ are considered respectively. For the non-Hopf case, we prove that the ruled real hypersurfaces of non-flat complex space forms do not admit Miao-Tam critical metrics. Finally, it is proved that a compact hypersurface of a complex Euclidean space admitting Miao-Tam critical metric with ${\lambda}$ > 0 or ${\lambda}$ < 0 is a sphere and a compact hypersurface of a non-flat complex space form does not exist such a critical metric.

CRITICAL KAHLER SURFACES

Kim, Jong-Su Korean Mathematical Society 1998 대한수학회보 Vol.35 No.3

We characterize real 4-dimensional Kahler metrices which are critical for natural quadratic Riemannian functionals defined on the space of all Riemannian metrics. In particular we show that such critical Kahler surfaces are either Einstein or have zero scalar curvature. We also make some discussion on criticality in the space of Kahler metrics.

CRITICAL POINT METRICS OF THE TOTAL SCALAR CURVATURE

Chang, Jeong-Wook,Hwang, Seung-Su,Yun, Gab-Jin Korean Mathematical Society 2012 대한수학회보 Vol.49 No.3

In this paper, we deal with a critical point metric of the total scalar curvature on a compact manifold $M$. We prove that if the critical point metric has parallel Ricci tensor, then the manifold is isometric to a standard sphere. Moreover, we show that if an $n$-dimensional Riemannian manifold is a warped product, or has harmonic curvature with non-parallel Ricci tensor, then it cannot be a critical point metric.

CRITICAL POINT METRICS OF THE TOTAL SCALAR CURVATURE

장정욱,황승수,윤갑진 대한수학회 2012 대한수학회보 Vol.49 No.3

In this paper, we deal with a critical point metric of the total scalar curvature on a compact manifold $M$. We prove that if the critical point metric has parallel Ricci tensor, then the manifold is isometric to a standard sphere. Moreover, we show that if an $n$-dimensional Riemannian manifold is a warped product, or has harmonic curvature with non-parallel Ricci tensor, then it cannot be a critical point metric.

Some rigidity characterizations of Einstein metrics as critical points for quadratic curvature functionals

Guangyue Huang,Bingqing Ma,Jie Yang 대한수학회 2020 대한수학회보 Vol.57 No.6

We study rigidity results for the Einstein metrics as the critical points of a family of known quadratic curvature functionals involving the scalar curvature, the Ricci curvature and the Riemannian curvature tensor, characterized by some pointwise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moreover, we also provide a few rigidity results for locally conformally flat critical metrics.

LOCALLY HOMOGENEOUS CRITICAL METRICS ON FOUR-DIMENSIONAL MANIFOLDS

Kang, Yu-Tae Korean Mathematical Society 2007 대한수학회지 Vol.44 No.1

We classify complete, locally homogeneous metrics with finite volume on four-dimensional manifolds which are critical points for the squared $L^2-norm$ functionals of either the full Riemannian curvature tensor or the Weyl curvature tensor defined on the space of Riemannian metrics.

IT BSC 기반의 서비스수준협약 측정지표, 핵심성공요인, 전략체계도 간 연계

이원창(Weon-chang Lee),김용겸(Yong-kyeon Kim) 한국인터넷전자상거래학회 2008 인터넷전자상거래연구 Vol.8 No.3

The purpose of this study is to analyze how to manage SLA related to IT BSC (balanced scorecard) as a means to establish an IT outsourcing management systems and to measure and manage business-centric IT services in order to maximize the effectiveness of IT outsourcing. IT BSC is used as a tool which regards IT as a supportive service for improving business performance and measures IT contribution in view of business value, external interest group utility, internal process efficiency (IT services supporting and operating efficiency), and learning/growth infra (technical contribution, education & training, etc.) in relation to CSF and SLA metrics. The results of this study are as follows: In order to develop SLA metrics related to business performance, we surveyed and analyzed A company's SLA operating case ('99-'06) and drew 47 metrics in 7 sections. A company, which was known for adopting and implementing the BSC systems successfully, was taken as a benchmarking company. By adding the 9 detailed metrics of which importance has been raised in MIS studies (IS performance measurement, etc.), 56 metrics in 7 sections were extracted. Finally 32 metrics considered to be continuously managed in view of business performance were selected by 13 experts in this area. By their assistances, we could find important evaluating factors (SLA metrics) and constructed the evaluation structure. We made the further analysis and study to extend the basic framework of A company. We classified SLA operating metrics by IT BSC 4 perspectives and presented IT BSC-based SLA strategy map in relation to CSF and SLA metrics. The results of this study offer an implication to IS consulting company in relation to strategic performance management.

Critical rimennian metrics on cosymplectic manifolds

Kim, Byung-Hak Korean Mathematical Society 1995 대한수학회지 Vol.32 No.3

In a Recent paper [3], D. Chinea, M. Delon and J. C. Marrero proved that a cosymplectic manifold is formal and constructed an example of compact cosymplectic manifold which is not a global product of a Kaehler manifold with the circle. In this paper we study the compact cosymplectic manifolds with critical Riemannian metrics.

RISKY MODULE PREDICTION FOR NUCLEAR I&C SOFTWARE

YOUNG-MI KIM,김현수 한국원자력학회 2012 Nuclear Engineering and Technology Vol.44 No.6

As software based digital I&C (Instrumentation and Control) systems are used more prevalently in nuclear plants,enhancement of software dependability has become an important issue in the area of nuclear I&C systems. Critical attributes of software dependability are safety and reliability. These attributes are tightly related to software failures caused by faults. Software testing and V&V (Verification and Validation) activities are hence important for enhancing software dependability. If the risky modules of safety-critical software can be predicted, it will be possible to focus on testing and V&V activities more efficiently and effectively. It should also make it possible to better allocate resources for regulation activities. We propose a prediction technique to estimate risky software modules by adopting machine learning models based on software complexity metrics. An empirical study with various machine learning algorithms was executed for comparing the prediction performance. Experimental results show SVMs (Support Vector Machines) perform as well or better than the other methods.