http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
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.
YANG-MILLS CONNECTIONS ON CLOSED LIE GROUPS
표용수,박준식,신영림 호남수학회 2010 호남수학학술지 Vol.32 No.4
In this paper, we obtain a necessary and sufficient con-dition for a left invariant connection in the tangent bundle over a closed Lie group with a left invariant metric to be a Yang-Mills con-nection. Moreover, we have a necessary and sufficient condition for a left invariant connection with a torsion-free Weyl structure in the tangent bundle over SU(2) with a left invariant Riemannian metric g to be a Yang-Mills connection.
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.
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.