• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.1113-1129
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• 2019

We define a class of semi-symmetric metric connection on a Riemannian manifold for which the conformal, the projective, the concircular, the quasi conformal and the m-projective curvature tensors are invariant. We also study the properties of semisymmetric, Ricci semisymmetric and Eisenhart problems for solving second order parallel symmetric and skew-symmetric tensors on the Riemannian manifolds equipped with a semi-symmetric metric P-connection.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.339-348
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• 2023

It is shown that every nilpotent-invariant module can be decomposed into a direct sum of a quasi-injective module and a square-free module that are relatively injective and orthogonal. This paper is also concerned with rings satisfying every cyclic right R-module is nilpotent-invariant. We prove that R ≅ R₁ × R₂, where R₁, R₂ are rings which satisfy R₁ is a semi-simple Artinian ring and R₂ is square-free as a right R₂-module and all idempotents of R₂ is central. The paper concludes with a structure theorem for cyclic nilpotent-invariant right R-modules. Such a module is shown to have isomorphic simple modules eR and fR, where e, f are orthogonal primitive idempotents such that eRf ≠ 0.

• Journal of the Korean Mathematical Society
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• v.24 no.2
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• pp.187-198
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• 1987

• Journal of the Korean Mathematical Society
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• v.27 no.2
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• pp.157-166
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• 1990

• Journal of the Korean Mathematical Society
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• v.25 no.2
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• pp.227-243
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• 1988

• Communications of the Korean Mathematical Society
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• v.2 no.1
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• pp.89-115
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• 1987

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.455-463
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• 1996

In [3] and [4], Kitahara, Pak and the author obtained the conformally invariant tensor $B_0$, which is an algebraic Hermitian analogue of the Weyl conformal curvature tensor W in the Riemannian geometry, by the decomposition of the curvature tensor H of the Hermitian connection and the notion of semi-curvature-like tensors of Tanno (see[7]). In [5], the author defined a conformally invariant tensor $B_0$ on a Hermitian manifold as a modification of $B_0$. Moreover he introduced the notion of local conformal Hermitian-flatness of Hermitian manifolds and proved that the vanishing of this tensor $B_0$ together with some condition for the scalar curvatures is a necessary and sufficient condition for a Hermitian manifold to be locally conformally Hermitian-flat.

• Honam Mathematical Journal
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• v.42 no.1
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• pp.123-137
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• 2020

The object of the present paper is to study certain geometrical properties of the submanifolds of generalized Sasakian space-forms. We deduce some results related to the invariant and anti-invariant slant submanifolds of the generalized Sasakian spaceforms. Finally, we study the properties of the sectional curvature, totally geodesic and umbilical submanifolds of the generalized Sasakian space-forms. To prove the existence of almost semiinvariant and anti-invariant submanifolds, we provide the non-trivial examples.

• Bulletin of the Korean Chemical Society
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• v.20 no.6
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• pp.720-726
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• 1999

It has been proved by the semi-classical gauge invariant formulation (GIF) that the correct interaction operator for coupling the field-free material states with the radiation field must be the position form regardless of the gauge chosen for expressing the electromagnetic potentials, in accordance with the well-established principle of gauge invariance. The semi-classical GIF is now extended to the quantized radiation field interacting with matter by defining the energy operator for the quantized radiation field in the presence of matter. It will be shown in this paper that the use of the energy operator guarantees the position form of the interaction operator even in the Coulomb gauge, contrary to the conventional approach in which the dark material Hamiltonian is used to get the interaction operator of the momentum form. The multipolar Hamiltonian is examined in the context of the quantum mechanical gauge transformation.

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.133-166
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• 2022

Let M be a semi-invariant submanifold with almost contact metric structure (𝜙, 𝜉, 𝜂, g) of codimension 3 in a complex space form M_n+1(c) for c ≠ 0. We denote by S and R_𝜉 be the Ricci tensor of M and the structure Jacobi operator in the direction of the structure vector 𝜉, respectively. Suppose that the third fundamental form t satisfies dt(X, Y) = 2𝜃g(𝜙X, Y) for a certain scalar 𝜃 ≠ 2c and any vector fields X and Y on M. In this paper, we prove that if it satisfies R_𝜉𝜙 = 𝜙R_𝜉 and at the same time S𝜉 = g(S𝜉, 𝜉)𝜉, then M is a real hypersurface in M_n(c) (⊂ M_n+1(c)) provided that $\bar{r}-2(n-1)c{\leq}0$, where $\bar{r}$ denotes the scalar curvature of M.