Jong Taek Cho

Bio: Jong Taek Cho is an academic researcher from Chonnam National University. The author has contributed to research in topics: Complex space & Ricci curvature. The author has an hindex of 18, co-authored 76 publications receiving 859 citations. Previous affiliations of Jong Taek Cho include Niigata University & Kyungpook National University.

Ricci solitons and real hypersurfaces in a complex space form

Abstract: We prove that a real hypersurface in a non-flat complex space form does not admit a Ricci soliton whose potential vector field is the Reeb vector field. Moreover, we classify a real hypersurface admitting so-called “$\eta$-Ricci soliton” in a non-flat complex space form.

On slant curves in sasakian 3-manifolds

Abstract: A classical theorem by Lancret says that a curve in Euclidean 3-space is of constant slope if and only if its ratio of curvature and torsion is constant. In this paper we study Lancret type problems for curves in Sasakian 3-manifolds.

Contact metric manifolds with η-parallel torsion tensor

Abstract: We show that a non-Sasakian contact metric manifold with η-parallel torsion tensor and sectional curvatures of plane sections containing the Reeb vector field different from 1 at some point, is a (k, μ)-contact manifold. In particular for the standard contact metric structure of the tangent sphere bundle the torsion tensor is η-parallel if and only if M is of constant curvature, in which case its associated pseudo-Hermitian structure is CR- integrable. Next we show that if the metric of a non-Sasakian (k, μ)-contact manifold (M, g) is a gradient Ricci soliton, then (M, g) is locally flat in dimension 3, and locally isometric to E n+1 × S n (4) in higher dimensions.

η-parallel contact metric spaces

Abstract: We prove that a contact metric manifold M = (M; η, ξ, ϕ, g) with η-parallel tensor h is either a K-contact space or a (k, µ)-space, where h denotes, up to a scaling factor, the Lie derivative of the structure tensor ϕ in the direction of the characteristic vector ξ . In the latter case, its associated CR-structure is in particular integrable.  2005 Elsevier B.V. All rights reserved. MSC: 53C15; 53C25; 54D10

Biharmonic curves in 3-dimensional Sasakian space forms

Abstract: We show that every proper biharmonic curve in a 3-dimensional Sasakian space form of constant holomorphic sectional curvature H is a helix (both of whose geodesic curvature and geodesic torsion are constants). In particular, if H ≠ 1, then it is a slant helix, that is, a helix which makes constant angle α with the Reeb vector field with the property \(\kappa^{2}+\tau^{2}=1+(H-1)\sin^{2}\alpha\). Moreover, we construct parametric equations of proper biharmonic herices in Bianchi–Cartan–Vranceanu model spaces of a Sasakian space form.

A short survey on biharmonic maps between Riemannian manifolds

Abstract: and the corresponding Euler-Lagrange equation is H = 0, where H is the mean curvature vector field. If φ : (M, g) → (N, h) is a Riemannian immersion, then it is a critical point of the bienergy in C∞(M,N) if and only if it is a minimal immersion [26]. Thus, in order to study minimal immersions one can look at harmonic Riemannian immersions. A natural generalization of harmonic maps and minimal immersions can be given by considering the functionals obtained integrating the square of the norm of the tension field or of the mean curvature vector field, respectively. More precisely: • biharmonic maps are the critical points of the bienergy functional E2 : C∞(M,N) → R, E2(φ) = 12 ∫

Almost Kenmotsu manifolds and local symmetry

Abstract: We consider locally symmetric almost Kenmotsu manifolds showing that such a manifold is a Kenmotsu manifold if and only if the Lie derivative of the structure, with respect to the Reeb vector field $\xi$, vanishes. Furthermore, assuming that for a $(2n+1)$-dimensional locally symmetric almost Kenmotsu manifold such Lie derivative does not vanish and the curvature satisfies $R_{XY}\xi =0$ for any $X, Y$ orthogonal to $\xi$, we prove that the manifold is locally isometric to the Riemannian product of an $(n+1)$-dimensional manifold of constant curvature $-4$ and a flat $n$-dimensional manifold. We give an example of such a manifold.