• Kyungpook Mathematical Journal
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• v.53 no.1
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• pp.49-86
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• 2013

This article is a continuation of the paper [21]. In this paper we deal with Maass-Jacobi forms on the Siegel-Jacobi space $\mathbb{H}{\times}\mathbb{C}^m$, where H denotes the Poincar$\acute{e}$ upper half plane and $m$ is any positive integer.

• East Asian mathematical journal
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• v.17 no.1
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• pp.103-114
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• 2001

When the target manifold is certain Kenmotsu manifolds, we characterize invariant immersions, tangential anti-invariant immersions and normal anti-invariant immersions by the spectra of the Jacobi operator.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.343-355
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• 2007

Using the modulus of smoothness ${\omega}^2_{{\varphi}^{\lambda}(f,t)_{\omega}$ Stechkin-Marchaud-Type inequalities with Jacobi weights of Bernstein Operators is established.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.373-382
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• 1997

When the target manifold is a Sasakian or cosympletic space form, we characterize invariant immersions, tangential anti-invariant immersions and normal anti-invariant immersions by the spectra of the Jacobi operator.

• Journal of the Korean Mathematical Society
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• v.34 no.2
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• pp.483-500
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• 1997

We investigate the geometric properties reflected by the spectra of the Jacobi operator of a harmonic map when the target manifold is a Riemannian product manifold or a Kaehlerian product manifold. And also we study the spectral characterization of Riemannian sumersions when the target manifold is $S^n \times S^n$ or $CP^n \times CP^n$.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.551-570
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• 2020

We introduce the notion of Lie invariant normal Jacobi operators for real hypersurfaces in the complex hyperbolic quadric Q^m∗ = SO^o_m,2/SO_mSO₂. The invariant normal Jacobi operator implies that the unit normal vector field N becomes 𝕬-principal or 𝕬-isotropic. Then in each case, we give a complete classification of real hypersurfaces in Q^m∗ = SO^o_m,2/SO_mSO₂ with Lie invariant normal Jacobi operators.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.317-336
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• 1998

We study real hypersurfaces of a complex space form such that the Jacobi operator with respect to the structure vector field and the structure tensor $\phi$ on the real hypersurface commute.

• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.547-566
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• 2003

In this paper, we introduce the notion of Maass-Jacobi forms and investigate some properties of these new automorphic forms. We also characterize these automorphic forms in several ways.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1595-1603
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• 2022

We show how some of well-known recurrent operators such as recurrent curvature operator, recurrent Ricci operator, recurrent Jacobi operator, recurrent shape and Weyl operators have the significant role for biharmonic hypersurfaces to be minimal in the Euclidean space.

• Honam Mathematical Journal
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• v.28 no.4
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• pp.573-589
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• 2006

Let M be a real hypersurface with almost contact metric structure $({\phi},{\xi},{\eta},g)$ in a non flat complex space form $M_n(c)$. In this paper, we prove that if the structure Jacobi operator $R_{\xi}$ is ${\xi}$-parallel and the Ricci tensor S commutes with the structure operator $\phi$, then a real hypersurface in $M_n(c)$ is a Hopf hypersurface. Further, we characterize such Hopf hypersurface in $M_n(c)$.