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Curvature homogeneity for four-dimensional manifolds
Sekigawa, Kouei,Suga, Hiroshi,Vanhecke, Lieven Korean Mathematical Society 1995 대한수학회지 Vol.32 No.1
Let (M,g) be an n-dimensional, connected Riemannian manifold with Levi Civita connection $\nabla$ and Riemannian curvature tensor R defined by $$ R_XY = [\nabla_X, \nabla_Y] - \nabla_{[X,Y]} $$ for all smooth vector fields X, Y. $\nablaR, \cdots, \nabla^kR, \cdots$ denote the successive covariant derivatives and we assume $\nabla^0R = R$.
Notes on tangent sphere bundles of constant radii
박정형,Kouei Sekigawa 대한수학회 2009 대한수학회지 Vol.46 No.6
We show that the Riemannian geometry of a tangent sphere bundle of a Riemannian manifold (M,g) of constant radius r reduces essentially to the one of unit tangent sphere bundle of a Riemannian manifold equipped with the respective induced Sasaki metrics. Further, we provide some applications of this theorem on the η-Einstein tangent sphere bundles and certain related topics to the tangent sphere bundles. We show that the Riemannian geometry of a tangent sphere bundle of a Riemannian manifold (M,g) of constant radius r reduces essentially to the one of unit tangent sphere bundle of a Riemannian manifold equipped with the respective induced Sasaki metrics. Further, we provide some applications of this theorem on the η-Einstein tangent sphere bundles and certain related topics to the tangent sphere bundles.
Orthogonal almost complex structures on the Riemannian products of even-dimensional round spheres
어은희,Kouei Sekigawa 대한수학회 2013 대한수학회지 Vol.50 No.2
We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and of a round 4-sphere.
A REMARK ON QUASI CONTACT METRIC MANIFOLDS
박정형,Kouei Sekigawa,신원민 대한수학회 2015 대한수학회보 Vol.52 No.3
As a natural generalization of the contact metric manifolds, Kim, Park and Sekigawa discussed quasi contact metric manifolds based on the geometry of the corresponding quasi K¨ahler cones. In this paper, we show that a quasi contact metric manifold is a contact manifold.
NOTES ON CRITICAL ALMOST HERMITIAN STRUCTURES
이정찬,박정형,Kouei Sekigawa 대한수학회 2010 대한수학회보 Vol.47 No.1
We discuss the critical points of the functional Fλ, μ (J, g) = ∫M (λτ+μτ* )dvg on the spaces of all almost Hermitian structures АН(M) with (λ,μ) ∈ R2 - (0,0),where τ and τ* being the scalar curvature and the *-scalar curvature of (J, g), respectively. We shall give several characterizations of Kähler structure for some special classes of almost Hermitian manifolds, in terms of the critical points of the functionals Fλ,μ(J,g) on АН(M). Further, we provide the almost Hermitian analogy of the Hilbert's result.
ORTHOGONAL ALMOST COMPLEX STRUCTURES ON THE RIEMANNIAN PRODUCTS OF EVEN-DIMENSIONAL ROUND SPHERES
Euh, Yunhee,Sekigawa, Kouei Korean Mathematical Society 2013 대한수학회지 Vol.50 No.2
We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and of a round 4-sphere.
A REMARK ON QUASI CONTACT METRIC MANIFOLDS
Park, JeongHyeong,Sekigawa, Kouei,Shin, Wonmin Korean Mathematical Society 2015 대한수학회보 Vol.52 No.3
As a natural generalization of the contact metric manifolds, Kim, Park and Sekigawa discussed quasi contact metric manifolds based on the geometry of the corresponding quasi $K{\ddot{a}}hler$ cones. In this paper, we show that a quasi contact metric manifold is a contact manifold.