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VARIATIONS OF THE LENGTH INTEGRAL
표용수,오원태,손희상 호남수학회 2014 호남수학학술지 Vol.36 No.1
In this paper, we obtain a necessary and sufficient condition for the second variation of an arbitrarily given smooth variation of a geodesic on a Riemannian manifold to be 0.
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On Ricci curvatures of left invariant metrics on SU(2)
표용수,Hyun Woong Kim,Joon-Sik Park 대한수학회 2009 대한수학회보 Vol.46 No.2
In this paper, we shall prove several results concerning Ricci curvature of a Riemannian manifold (M,g): =(SU(2), g) with an arbitrary given left invariant metric g. First of all, we obtain the maximum (resp. minimum) of { r(X) := Ric(X,X) | ||X||_g =1, X∈Χ(M) } where $Ric$ is the Ricci tensor field on (M,g), and then get a necessary and sufficient condition for the Levi-Civita connection ▽ on the manifold (M,g) to be projectively flat. Furthermore, we obtain a necessary and sufficient condition for the Ricci curvature r(X) to be always positive (resp. negative), independently of the choice of unit vector field X. In this paper, we shall prove several results concerning Ricci curvature of a Riemannian manifold (M,g): =(SU(2), g) with an arbitrary given left invariant metric g. First of all, we obtain the maximum (resp. minimum) of { r(X) := Ric(X,X) | ||X||_g =1, X∈Χ(M) } where $Ric$ is the Ricci tensor field on (M,g), and then get a necessary and sufficient condition for the Levi-Civita connection ▽ on the manifold (M,g) to be projectively flat. Furthermore, we obtain a necessary and sufficient condition for the Ricci curvature r(X) to be always positive (resp. negative), independently of the choice of unit vector field X.
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표용수,조성진,정진문,박진한,Pyo, Yong-Soo,Cho, Sung-Jin,Jeong, Jin-Mun,Park, Jin-Han 영남수학회 2010 East Asian mathematical journal Vol.26 No.2
There are serious difficulties with management of general mathematics education courses because of enormous gap between freshman's ability of mathematics and lack of problem solving ability. In this paper, we try to find methods so we can reduce the difficulties. By utilizing students survey, management of Mathematics Cafe and setting example classes for Calculus and Linear Algebra we suggest effective management strategies and teaching-learning methods.
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표용수,박준식 대한수학교육학회 2011 수학교육학연구 Vol.21 No.1
The purpose of this paper is to investigate the effects on academic achievement for university basic mathe- matics in order to improve the problem-solving abilities of low achievement students in university general mathematics. In this paper, we suggest effective management strategies and teaching-learning methods according to level-based classes with utilizing scholastic level assessment, students survey, Mathematics Cafe and tutorial program, and also managing demonstration classes which are using Webwork system for assign- ments and evaluating the class. P대학에서는 자연계열 신입생을 대상으로 수학 진단평가를 실시하여, 일정 점수를 취득하지 못한 학생들과 미응시자를 대상으로 수학 기초학력 부진학생들의 문제해결력 향상과 학력증진을 위해 개설한 기초수학및연습 교과목을 필히 수강하도록 하고 있다. 본 논문에서는 기초수학및연습 수강학생을 25개의 수준별 학급으로 편성하여 운영한 결과를 토대로 해당 교과목의 효율적 학습지도 방안과 수준별 학급 운영에 대한 유의점 및 개선방안을 제안한다.
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SCALAR CURVATURES ON SU(3)/T (k, l)
표용수,신현주,박준식 호남수학회 2011 호남수학학술지 Vol.33 No.4
In this paper, we estimated the Ricci curvature and the scalar curvature on SU(3)/T(k, l) under the condition (k, l) ∈ R^2 (|k| + |l| ≠ 0), where the four isotropy irreducible representations in SU(3)/T(k, l) are, not necessarily, mutually equivalent or inequivalent.
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ON STABILITY OF EINSTEIN WARPED PRODUCT MANIFOLDS
표용수,김현웅,박준식 호남수학회 2010 호남수학학술지 Vol.32 No.1
Let (B, □) and (N,□) be Einstein manifolds. Then, we get a complete (necessary and su±cient) condition for the warped product manifold B× fN := (B × N,□+ f□) to be Einstein, and obtain a complete condition for the Einstein warped product man-ifold B £f N to be weakly stable. Moreover, we get a complete condition for the map i : (B,□)× (N,□) → B ×fN, 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 × fN to be Einstein.
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