• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.557-584
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• 2024

An almost complex torus manifold is a 2n-dimensional compact connected almost complex manifold equipped with an effective action of a real n-dimensional torus Tⁿ ≃ (S¹)ⁿ that has fixed points. For an almost complex torus manifold, there is a labeled directed graph which contains information on weights at the fixed points and isotropy spheres. Let M be a 6-dimensional almost complex torus manifold with Euler number 6. We show that two types of graphs occur for M, and for each type of graph we construct such a manifold M, proving the existence. Using the graphs, we determine the Chern numbers and the Hirzebruch χ_y-genus of M.

• Korean Journal of Mathematics
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• v.32 no.2
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• pp.315-328
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• 2024

The aim of the paper is to study an η-Einstein soliton on (2n + 1)-dimensional (k, µ)-contact metric manifold. At first, we establish various results related to (2n + 1)-dimensional (k, µ)-contact metric manifold that exhibit an η-Einstein soliton. Next we study some curvature conditions admitting an η-Einstein soliton on (2n+1)-dimensional (k, µ)-contact metric manifold. Furthermore, we consider specific conditions associated with an η-Einstein soliton on (2n+1)-dimensional (2n+1)-dimensional (k, µ)-contact metric manifold. Finally, we show the existance of an η-Einstein soliton on (k, µ)-contact metric manifold.

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

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

• Honam Mathematical Journal
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• v.32 no.3
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• pp.363-374
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• 2010

We define a semi-symmetric metric connection in an almost r-paracontact Riemannian manifold and we consider submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric metric connection and obtain Gauss and Codazzi equations, Weingarten equation and curvature tensor for submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric metric connection.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.507-520
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• 2009

The object of the present paper is to study conformally at almost pseudo Ricci symmetric manifolds. The existence of a conformally at almost pseudo Ricci symmetric manifold with non-zero and non-constant scalar curvature is shown by a non-trivial example. We also show the existence of an n-dimensional non-conformally at almost pseudo Ricci symmetric manifold with vanishing scalar curvature.

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.761-765
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• 2012

We prove that for a toric manifold (respectively, a quasitoric manifold) M, any graded ring isomorphism $H^*(M){\rightarrow}H^*({\Pi}_{i=1}^{m}\mathbb{C}P^{ni})$ can be realized by a diffeomorphism (respectively, a homeomorphism) ${\Pi}_{i=1}^{m}\mathbb{C}P^{ni}{\rightarrow}M$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.883-899
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• 2014

We introduce GCR-lightlike submanifold of a semi-Riemannian product manifold and give an example. We study geodesic GCR-lightlike submanifolds of a semi-Riemannian product manifold and obtain some necessary and sufficient conditions for a GCR-lightlike submanifold to be a GCR-lightlike product. Finally, we discuss minimal GCR-lightlike submanifolds of a semi-Riemannian product manifold.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.515-531
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• 2018

Jin studied lightlike hypersurfaces of an indefinite Kaehler manifold [6, 8] or indefinite trans-Sasakian manifold [7] with a quarter-symmetric metric connection. Jin also studied generic lightlike submanifolds of an indefinite trans-Sasakian manifold with a quarter-symmetric metric connection [10]. We study generic lightlike submanifolds of an indefinite Kaehler manifold with a quarter-symmetric metric connection.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.75-85
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• 2018

In this paper, we study nonconstant warping functions on an Einstein warped product manifold $M=B{\times}_{f^2}F$ with a warped product metric $g=g_B+f(t)^2g_F$. And we consider a 2-dimensional base manifold B with a metric $g_B=dt^2+(f^{\prime}(t))^2du^2$. As a result, we prove the following: if M is an Einstein warped product manifold with a 2-dimensional base, then there exist generally nonconstant warping functions f(t).

• Journal of the Chungcheong Mathematical Society
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• v.22 no.4
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• pp.653-665
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• 2009

We define a semi-symmetric non-metric connection in an almost r-paracontact Riemannian manifold and we consider submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric non-metric connection and obtain Gauss and Codazzi equations, Weingarten equation and curvature tensor for submanifolds of an almost r-paracontact Riemannian manifold endowed with a semi-symmetric non-metric connection.