• Bulletin of the Korean Mathematical Society
• /
• v.53 no.6
• /
• pp.1869-1878
• /
• 2016

We study closed Einstein-Weyl structure on compact K-contact manifolds and prove that a compact K-contact manifold admitting a closed Einstein-Weyl structure is Einstein and Sasakian.

• Kyungpook Mathematical Journal
• /
• v.21 no.2
• /
• pp.243-250
• /
• 1981

• Kyungpook Mathematical Journal
• /
• v.10 no.2
• /
• pp.161-164
• /
• 1970

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.4
• /
• pp.713-724
• /
• 2005

We prove that a (k, $\mu$)-manifold with vanishing E­Bochner curvature tensor is a Sasakian manifold. Several interesting corollaries of this result are drawn. Non-Sasakian (k, $\mu$)­manifolds with C-Bochner curvature tensor B satisfying B $(\xi,\;X)\;\cdot$ S = 0, where S is the Ricci tensor, are classified. N(K)-contact metric manifolds $M^{2n+1}$, satisfying B $(\xi,\;X)\;\cdot$ R = 0 or B $(\xi,\;X)\;\cdot$ B = 0 are classified and studied.

• Communications of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.261-272
• /
• 2018

The object of the present paper is to study some curvature properties of almost Kenmotsu manifolds with conformal Reeb foliation. Among others it is proved that an almost Kenmotsu manifold with conformal Reeb foliation is Ricci semisymmetric if and only if it is an Einstein manifold. Finally, we study Yamabe soliton in this manifold.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.5
• /
• pp.1299-1306
• /
• 2020

An almost contact metric manifold is called a quasi contact metric manifold if the corresponding almost Hermitian cone is a quasi Kähler manifold, which was introduced by Y. Tashiro [9] as a contact O*-manifold. In this paper, we show that a quasi contact metric manifold with Killing characteristic vector field is a K-contact manifold. This provides an extension of the definition of K-contact manifold.

• Kyungpook Mathematical Journal
• /
• v.45 no.2
• /
• pp.231-240
• /
• 2005

The paper shows that a hypersurface with constant curvature with the condition $hD{\subset}D$, of a contact metric manifold with a nullity condition and ${\varphi}-constant$ sectional curvature, has the curvature equals to k and ${\mu}=0$.

• Journal of applied mathematics & informatics
• /
• v.40 no.3_4
• /
• pp.741-751
• /
• 2022

The object of the present paper is to study some geometric properties of invariant submanifolds of N(k)-contact metric manifold admitting generalized Tanaka-Webster connection.

• Journal of the Korean Mathematical Society
• /
• v.42 no.5
• /
• pp.1101-1110
• /
• 2005

Recently, Chen studied warped products which are CR-submanifolds in Kaehler manifolds and established general sharp inequalities for CR-warped products in Kaehler manifolds. In the present paper, we obtain sharp estimates for the squared norm of the second fundamental form (an extrinsic invariant) in terms of the warping function for contact CR-warped products isometrically immersed in Kenmotsu space forms. The equality case is considered. Some applications are derived.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.1
• /
• pp.109-116
• /
• 2007

We study an (n+1)($(n{\geq}3)$-dimensional contact CR-submanifold of (n-1) contact CR-dimension in a (2m+1)-unit sphere $S^{2m+1}$, and to determine such sub manifolds under conditions concerning the second fundamental form and the induced almost contact structure.