• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.109-126
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• 2012

In 2003, Marques-Smith and Sullivan described the join ${\Omega}$ of the 'natural order' $\leq$ and the 'containment order' $\subseteq$ on P(X), the semigroup under composition of all partial transformations of a set X. And, in 2004, Pinto and Sullivan described all automorphisms of PS(q), the partial Baer-Levi semigroup consisting of all injective ${\alpha}{\in}P(X)$ such that ${\mid}X{\backslash}X{\alpha}\mid=q$, where $N_0{\leq}q{\leq}{\mid}X{\mid}$. In this paper, we describe the group of automorphisms of R(q), the largest regular subsemigroup of PS(q). In 2010, we studied some properties of $\leq$ and $\subseteq$ on PS(q). Here, we characterize the meet and join under those orders for elements of R(q) and PS(q). In addition, since $\leq$ does not equal ${\Omega}$ on I(X), the symmetric inverse semigroup on X, we formulate an algebraic version of ${\Omega}$ on arbitrary inverse semigroups and discuss some of its properties in an algebraic setting.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.161-166
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• 2005

Let BQ be the class of all semigroups whose bi-ideals are quasi-ideals. It is known that regular semigroups, right [left] 0-simple semigroups and right [left] 0-simple semigroups belong to BQ. Every zero semigroup is clearly a member of this class. In this paper, we characterize when generalized full transformation semigroups and generalized Baer-Levi semigroups are in BQ in terms of the cardinalities of sets.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.843-852
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• 2013

The characteristic connection is a good substitute for Levi-Civita connection in studying non-integrable geometries. In this paper we consider the homogeneous space $U(3)/(U(1){\times}U(1){\times}U(1))$ with a one-parameter family of Hermitian structures. We prove that the one-parameter family of Hermtian structures admit a characteristic connection. We also compute the torsion of the characteristic connecitons.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.781-793
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• 2012

We study some properties of a semi-Riemannian submanifold of a semi-Riemannian manifold with a semi-symmetric non-metric connection. Then, we prove that the Ricci tensor of a semi-Riemannian submanifold of a semi-Riemannian space form admitting a semi-symmetric non-metric connection is symmetric but is not parallel. Last, we give the conditions under which a totally umbilical semi-Riemannian submanifold with a semi-symmetric non-metric connection is projectively flat.

• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.93-101
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• 1995

Let (M,g) be an n-dimensional, connected Riemannian manifold with Levi Civita connection $\nabla$ and Riemannian curvature tensor R defined by $$ R_XY = [\nabla_X, \nabla_Y] - \nabla_{[X,Y]} $$ for all smooth vector fields X, Y. $\nablaR, \cdots, \nabla^kR, \cdots$ denote the successive covariant derivatives and we assume $\nabla^0R = R$.

• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.87-99
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• 2001

We prove that the germ of a CR mapping f between real analytic real hypersurfaces has a holomorphic extension and satisfies a complete system of finite order if the source is of finite type in the sense of Bloom-Graham and the target is k-nondegenerate under certain generic assumptions on f.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1441-1456
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• 2017

We consider a 3-dimensional Riemannian manifold M with a circulant metric g and a circulant structure q satisfying $q^3=id$. The structure q is compatible with g such that an isometry is induced in any tangent space of M. We introduce three classes of such manifolds. Two of them are determined by special properties of the curvature tensor. The third class is composed by manifolds whose structure q is parallel with respect to the Levi-Civita connection of g. We obtain some curvature properties of these manifolds (M, g, q) and give some explicit examples of such manifolds.

• Bulletin of the Korean Mathematical Society
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• v.30 no.1
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• pp.17-23
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• 1993

In this paper, we will discuss on the above problem for the case that .upsilon. is a Riemannian foliation. If .upsilon. is a Riemannian foliation on (M, g), we derive some basic relations between the curvature $R^{D}$ of the normal connection D and the curvature R of the Levi-Civita connection .del. on (M, g) (see Lemma 1).).

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.725-733
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• 2011

The characteristic connection is a good substitute for the Levi-Civita connection, especially in studying non-integrable geometries. Unfortunately, not every geometric structure has the characteristic connection. In this paper we consider the space $U(3)/(U(1){\times}U(1){\times}U(1))$ with an almost Hermitian structure and prove that it has a geometric structure admitting the characteristic connection.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.575-592
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• 2021

In this paper, we introduce the Berger type deformed Sasaki metric on the cotangent bundle T^*M over an anti-paraKähler manifold (M, 𝜑, g) as a new natural metric with respect to g non-rigid on T^*M. Firstly, we investigate the Levi-Civita connection of this metric. Secondly, we study the curvature tensor and also we characterize the scalar curvature.