• 충청수학회지
• /
• 제13권1호
• /
• pp.65-70
• /
• 2000

The purpose of this paper is to apply the extremal length to conformal mappings. We drive an interesting formula of Gr$\ddot{o}$tzsch by an alternative simple method.

• 대한수학회논문집
• /
• 제13권3호
• /
• pp.539-544
• /
• 1998

Let (M, g) be a noncompact complete Riemannian manifold of dimension n $\geq$ 3 with scalar curvature S, which is close to O. With conditions on a conformal invariant and scalar curvature of (M, g), we show that there exists a conformal metric (equation omitted), near g, whose scalar curvature (equation omitted) = 0 by gluing solutions of the corresponding partial differential equation on each bounded subsets $K_{i}$ with ∪$K_{i}$ = M.

• 대한수학회지
• /
• 제22권2호
• /
• pp.97-102
• /
• 1985

• 대한수학회지
• /
• 제11권2호
• /
• pp.135-139
• /
• 1974

• 대한수학회보
• /
• 제27권2호
• /
• pp.133-142
• /
• 1990

In this paper, we define a new tensor field on a Sasqakian manifold, which is constructed from the conformal curvature tensor field by using the Boothby-Wang's fibration ([3]), and study some properties of this new tensor field. In Section 2, we recall definitions and fundamental properties of Sasakian manifold and .phi.-holomorphic sectional curvature. In Section 3, we define contact conformal curvature tensor field on a Sasakian manifold and prove that it is invariant under D-homothetic deformation due to S. Tanno([13]). In Section 4, we study Sasakian manifolds with vanishing contact conformal curvature tensor field, and the last Section 5 is devoted to studying some properties of fibred Riemannian spaces with Sasakian structure of vanishing contact conformal curvature tensor field.

• 대한수학회보
• /
• 제44권4호
• /
• pp.795-806
• /
• 2007

We investigate F-traceless component of the conformal curvature tensor defined by (3.6) in $K\ddot{a}hler$ manifolds of dimension ${\geq}4$, and show that the F-traceless component is invariant under concircular change. In particular, we determine $K\ddot{a}hler$ manifolds with parallel F-traceless component and improve some theorems, provided in the previous paper([2]), which are concerned with the traceless component of the conformal curvature tensor and the spectrum of the Laplacian acting on $p(0{\leq}p{\leq}2)$-forms on the manifold by using the F-traceless component.

• 충청수학회지
• /
• 제12권1호
• /
• pp.193-196
• /
• 1999

In this note, we present some geometric applications of extremal length to analytic functions. We drive an interesting formula by the method of extremal length.

• 대한수학회지
• /
• 제56권4호
• /
• pp.1113-1129
• /
• 2019

We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the m-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric P-connection.

• 대한수학회지
• /
• 제31권4호
• /
• pp.629-632
• /
• 1994

Let (M, g) be a Riemannian manifold. The relation between a (pointwise) conformal metric of the metric g and the scalar curvature of this new metrics is investigated by Kazdan, Warner and Schoen (cf. [1, 4]).

• 대한수학회지
• /
• 제61권2호
• /
• pp.341-356
• /
• 2024

In this paper, apply the regularities of the fractional Poisson kernels, we establish the Sobolev type trace inequalities of homogeneous Besov spaces, which are invariant under the conformal transforms. Also, by the aid of the Carleson measure characterizations of Q type spaces, the local version of Sobolev trace inequalities are obtained.