• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.367-376
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• 2006

We investigate semi-symmetry and pseudo-symmetry of some 3-dimensional Riemannian manifolds: the D'Atri spaces, the Thurston geometries as well as the ${\eta}$-Einstein manifolds. We prove that all these manifolds are pseudo-symmetric and that many of them are not semi-symmetric.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.757-767
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• 1998

For a Riemannian manifold $(M^n, g)$ we consider the space $V(M^n, g)$ of all smooth functions on $M^n$ whose Hessian is proportional to the metric tensor $g$. It is well-known that if $M^n$ is a space form then $V(M^n)$ is of dimension n+2. In this paper, conversely, we prove that if $V(M^n)$ is of dimension $\ge{n+1}$, then $M^n$ is a Riemannian space form.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.273-284
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• 2001

Let P be a spacelike (n-2)-dimensional submanifold of an n-dimensional Lorentz manifold M and let$\sigma$ be a P-normal null geodesic with Ric($\sigma',\sigma'$)$\geq$m, for the any given nonpositive constant m. We establish a sufficient condition such that there is a focal point of P along $\sigma$.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.539-552
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• 2020

In this paper we consider gradient almost Ricci solitons with weak conditions on Weyl and Bach tensors. We show that a gradient almost Ricci soliton has harmonic Weyl curvature if it has fourth order divergence-free Weyl tensor, or it has divergence-free Bach tensor. Furthermore, if its Weyl tensor is radially flat, we prove such a gradient almost Ricci soliton is locally a warped product with Einstein fibers. Finally, we prove a rigidity result on compact gradient almost Ricci solitons satisfying an integral condition.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.655-667
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• 2012

In this paper, we deal with a critical point metric of the total scalar curvature on a compact manifold $M$. We prove that if the critical point metric has parallel Ricci tensor, then the manifold is isometric to a standard sphere. Moreover, we show that if an $n$-dimensional Riemannian manifold is a warped product, or has harmonic curvature with non-parallel Ricci tensor, then it cannot be a critical point metric.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.857-864
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• 2009

The special conformally flatness is a generalization of a sub-projective space. B. Y. Chen and K. Yano ([4]) showed that every canal hypersurface of a Euclidean space is a special conformally flat space. In this paper, we study the conditions for the base space B is special conformally flat in the conharmonically flat warped product space $B^n{\times}f\;R^1$.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.471-484
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• 2005

We study Riemannian or pseudo-Riemannian manifolds which carry the space of closed conformal vector fields of at least 2-dimension. Subject to the condition that at each point the set of closed conformal vector fields spans a non-degenerate subspace of the tangent space at the point, we prove a global and a local classification theorems for such manifolds.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.585-594
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• 2022

In this article we classify four dimensional gradient Ricci solitons (M, g, f) with half harmonic Weyl curvature and at most two distinct Ricci-eigenvalues at each point. Indeed, we showed that, in a neighborhood V of each point in some open dense subset of M, (V, g) is isometric to one of the following: (i) an Einstein manifold. (ii) a domain in the Riemannian product (ℝ², g₀) × (N, ${\tilde{g}}$), where g₀ is the flat metric on ℝ² and (N, ${\tilde{g}}$) is a two dimensional Riemannian manifold of constant curvature λ ≠ 0. (iii) a domain in ℝ × W with the warped product metric $ds^2+h(s)^2{\tilde{g}}$, where ${\tilde{g}}$ is a constant curved metric on a three dimensional manifold W.

• The Journal of the Acoustical Society of Korea
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• v.14 no.4
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• pp.21-28
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• 1995

In this paper an intonation conversion method is presented which provides the basic study on converting the original speech into the artificially intoned one. This method employs the other speaker's excitation signals as intonation information and the original vocal tract spectra, which are warped with the other speaker's ones by using DTW. as vocal features, and intonation converted speech signals are synthesized through short-time inverse Fourier transform(STIFT) of their product. To evaluate the intonation converted speech by this method, we collect Korean single vowels and sentences spoken by 30 males and compare fundamental frequency contours spectrograms, distortion measures and MOS test between the original speech and the converted one. The result shows that this method can convert and speech into the intoned one of the other speaker's.