• The Pure and Applied Mathematics
• /
• v.5 no.1
• /
• pp.79-86
• /
• 1998

In this paper, we study an (n ＋ 1)-dimensional compact, orientable, minimal contact CR-submanifold of (n - 1) ontact CR-dimension in a (2m ＋ 1)-dimensional unit sphere $S^{2m＋1}$ in terms of integral formula.

• Journal of the Korean Mathematical Society
• /
• v.44 no.2
• /
• pp.373-391
• /
• 2007

We study an (n+3)($n\;{\geq}\;7-dimensional$ real submanifold of a (4m+3)-unit sphere $S^{4m+3}$ with Sasakian 3-structure induced from the canonical quaternionic $K\"{a}hler$ structure of quaternionic (m+1)-number space $Q^{m+1}$, and especially determine contact three CR-submanifolds with (p-1) contact three CR-dimension under the equality conditions given in (4.1), where p = 4m - n denotes the codimension of the submanifold. Also we provide necessary conditions concerning sectional curvature in order that a compact contact three CR-submanifold of (p-1) contact three CR-dimension in $S^{4m+3}$ is the model space $S^{4n_1+3}(r_1){\times}S^{4n_2+3}(r_2)$ for some portion $(n_1,\;n_2)$ of (n-3)/4 and some $r_1,\;r_2$ with $r^{2}_{1}+r^{2}_{2}=1$.

• Journal of the Korean Mathematical Society
• /
• v.47 no.3
• /
• pp.505-521
• /
• 2010

Alfred Gray introduced in [8] three curvature identities for the class of almost Hermitian manifolds. Using the warped product construction and the Boothby-Wang fibration we will give an equivalent of these identities for the class of almost contact metric manifolds.

• Journal of the Korean Mathematical Society
• /
• v.42 no.5
• /
• pp.883-892
• /
• 2005

We classify N($\kappa$)-contact metric manifolds which satisfy $Z(\xi,\;X)\cdotZ\;=\;0,\;Z(\xi,\;X)\cdotR\;=\;0\;or\;R(\xi,\;X)\cdotZ\;=\;0$.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.3
• /
• pp.541-549
• /
• 2010

In this paper we derive an integral formula on an (n + 1)-dimensional, compact, minimal contact CR-submanifold M of (n - 1) contact CR-dimension immersed in a unit (2m+1)-sphere $S^{2m+1}$. Using this integral formula, we give a sufficient condition concerning with the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

• 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.

• Communications of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.251-260
• /
• 2020

In this paper, we show that it is Chen surfaces that non-minimal pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in S⁵. Moreover, we show that pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in S⁵ are the locally product of two pseudo-Hermitian circles.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.949-966
• /
• 2009

We proved in [10] that Friedrich's estimate [5] for the first eigenvalue of the Dirac operator can be improved when a Codazzi tensor exists. In the paper we further prove that his estimate can be improved as well via a well-chosen divergencefree symmetric tensor. We study the geometric implication of the new first eigenvalue estimates over Sasakian spin manifolds and show that some particular types of spinors appear as the limiting case.

• Kyungpook Mathematical Journal
• /
• v.51 no.4
• /
• pp.457-468
• /
• 2011

We consider pseudo-symmetric and Ricci generalized pseudo-symmetric N(${\kappa}$) contact metric manifolds. We also consider N(${\kappa}$)-contact metric manifolds satisfying the condition $S{\cdot}R$ = 0 where R and S denote the curvature tensor and the Ricci tensor respectively. Finally we give some examples.

• Communications of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.1315-1328
• /
• 2019

The object of the present paper is to study ${\eta}$-recurrent ${\ast}$-Ricci tensor, ${\ast}$-Ricci semisymmetric and globally ${\varphi}-{\ast}$-Ricci symmetric contact metric generalized (${\kappa}$, ${\mu}$)-space form. Besides these, ${\ast}$-Ricci soliton and gradient ${\ast}$-Ricci soliton in contact metric generalized (${\kappa}$, ${\mu}$)-space form have been studied.