• Honam Mathematical Journal
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• v.42 no.4
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• pp.733-745
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• 2020

The object of the present paper is to study the almost Hermitian submersion from an almost Hermitian manifold admits a Ricci soliton. Where, we investigate any fibre of such a submersion is a Ricci soliton or Einstein. We also get necessary conditions for which the base manifold of an almost Hermitian submersion is a Ricci soliton or Einstein. Moreover, we obtain the harmonicity of an almost Hermitian submersion from a Ricci soliton to an almost Hermitian manifold.

• 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.

• East Asian mathematical journal
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• v.26 no.5
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• pp.649-654
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• 2010

A positive definite Hermitian lattice is said to be 2-universal if it represents all positive definite binary Hermitian lattices. We find some finiteness theorems which ensure 2-universality of Hermitian lattices over several imaginary quadratic number fields.

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.289-294
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• 2009

We show that on a Hermitian surface M, if M is weakly *-Einstein and has J-invariant Ricci tensor then M is Einstein, and vice versa. As a consequence, we obtain that a compact *-Einstein Hermitian surface with J-invariant Ricci tensor is $K{\ddot{a}}hler$. In contrast with the 4- dimensional case, we show that there exists a compact Einstein Hermitian (4n + 2)-dimensional manifold which is not weakly *-Einstein.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.51-67
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• 2004

A matrix pair $(X_0,\;Y_0)$ is called a Hermitian nonnegative-definite(respectively, positive-definite) solution to the matrix equation $GXG^*\;+\;HYH^*\;=\;C$ with unknown X and Y if $X_{0}$ and $Y_{0}$ are Hermitian nonnegative-definite (respectively, positive-definite) and satisfy $GX_0G^*\;+\;HY_0H^*\;=\;C$. Necessary and sufficient conditions for the existence of at least a Hermitian nonnegative-definite (respectively, positive-definite) solution to the matrix equation are investigated. A representation of the general Hermitian nonnegative-definite (respectively positive-definite) solution to the equation is also obtained when it has such solutions. Two presented examples show these advantages of the proposed approach.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.251-260
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• 2020

In this paper, we show that it is Chen surfaces that non-minimal pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in S⁵. Moreover, we show that pseudo-Hermitian mass-symmetric 2-type Legendre surfaces in S⁵ are the locally product of two pseudo-Hermitian circles.

• The Pure and Applied Mathematics
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• v.18 no.3
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• pp.185-199
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• 2011

In this paper, we present a new extended Jacobi method for computing eigenvalues and eigenvectors of Hermitian matrices which does not use any complex arithmetics. This method can be readily applied to skew-Hermitian and real skew-symmetric matrices as well. An example illustrating its computational efficiency is given.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.585-593
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• 1996

We make the definition of hermitian K-theory for nonunital rings which makes as many senses as possible. We next show that the excision property in rational hermitian K-theory implies the nullity of rational $H B^-$-homology which is the antisymmetric part of Bar homology.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.119-128
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• 2013

In the present paper, we define a product-symmetric recurrent-metric connection in an almost Hermitian manifold and study some properties of this connection, in particular, its curvature properties.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.587-601
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• 2015

In this paper, we investigate the $\mathbb{R}$-complex Hermitian Finsler spaces, emphasizing the differences that separate them from the complex Finsler spaces. The tools used in this study are the Chern-Finsler and Berwald connections. By means of these connections, some classes of the $\mathbb{R}$-complex Hermitian Finsler spaces are defined, (e.g. weakly K$\ddot{a}$hler, K$\ddot{a}$hler, strongly K$\ddot{a}$hler). Here the notions of K$\ddot{a}$hler and strongly K$\ddot{a}$hler do not coincide, unlike the complex Finsler case. Also, some kinds of Berwald notions for such spaces are introduced. A special approach is devoted to obtain the equivalence conditions for an $\mathbb{R}$-complex Hermitian Finsler space to become a weakly Berwald or Berwald. Finally, we obtain the conditions under which an $\mathbb{R}$-complex Hermitian Finsler space with Randers metric is Berwald. We get some clear examples which illustrate the interest for this work.