• Kyungpook Mathematical Journal
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• v.29 no.1
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• pp.11-25
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• 1989

• Bulletin of the Korean Mathematical Society
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• v.47 no.1
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• pp.167-178
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• 2010

We discuss the critical points of the functional $F_{\lambda,\mu}(J,g)=\int_M(\lambda\tau+\mu\tau^*)d\upsilon_g$ on the spaces of all almost Hermitian structures AH(M) with $(\lambda,\mu){\in}R^2-(0,0)$, where $\tau$ and $\tau^*$ being the scalar curvature and the *-scalar curvature of (J, g), respectively. We shall give several characterizations of Kahler structure for some special classes of almost Hermitian manifolds, in terms of the critical points of the functionals $F_{\lambda,\mu}(J,g)$ on AH(M). Further, we provide the almost Hermitian analogy of the Hilbert's result.

• Bulletin of the Korean Mathematical Society
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• v.42 no.2
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• pp.405-413
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• 2005

We consider the connections $\nabla$ on the Rizza manifold (M, J, L) satisfying ${\nabla}G=0\;and\;{\nabla}J=0$. Among them, we derive a Lichnerowicz connection from the Cart an connection and characterize it in terms of torsion. Generalizing Kahler condition in Hermitian geometry, we define a Kahler condition for Rizza manifolds. For such manifolds, we show that the Cartan connection and the Lichnerowicz connection coincide and that the almost complex structure J is integrable.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1327-1340
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• 2019

We establish a monotonicity formula of V-harmonic maps by using the stress-energy tensor. Use the monotonicity formula, we can derive a Liouville type theorem for V-harmonic maps. As applications, we also obtain monotonicity and constancy of Weyl harmonic maps from conformal manifolds to Riemannian manifolds and ${\pm}holomorphic$ maps between almost Hermitian manifolds. Finally, a constant boundary-value problem of V-harmonic maps is considered.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.137-145
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• 2004

In [13], we developed a theory of complex Finsler manifolds to investigate the global geometry of complex Finsler manifolds. There we proved a version of Bonnet-Myers' theorem for complex Finsler manifolds with a certain condition on the Finsler metric which is a generalization of the Kahler condition for the Hermitian metric. In this paper, we show that if the holomorphic sectional curvature of M is ${\geq}\;c^2\;>\;0$, then M is simply connected. This is a generalization of the Synge's theorem in the Riemannian geometry and the Tsukamoto's theorem for Kahler manifolds. The main point of the proof lies in how we can circumvent the convex neighborhood theorem in the Riemannian geometry. A second variation formula of arc length for complex Finsler manifolds is also derived.

• 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.1
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• pp.173-187
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• 2021

In this paper, we deal with the notion of a v-semi-slant submersion from an almost Hermitian manifold onto a Riemannian manifold. We investigate the integrability of distributions, the geometry of foliations, and a decomposition theorem. Given such a map with totally umbilical fibers, we have a condition for the fibers of the map to be minimal. We also obtain an inequality of a proper v-semi-slant submersion in terms of squared mean curvature, scalar curvature, and a v-semi-slant angle. Moreover, we give some examples of such maps and some open problems.

• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.951-962
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• 2013

We introduce semi-slant submersions from almost Hermitian manifolds onto Riemannian manifolds as a generalization of slant submersions, semi-invariant submersions, anti-invariant submersions, etc. We obtain characterizations, investigate the integrability of distributions and the geometry of foliations, etc. We also find a condition for such submersions to be harmonic. Moreover, we give lots of examples.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.795-809
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• 2020

In the present paper, we introduce the notion of quasi hemi-slant submanifolds of almost Hermitian manifolds and give some of its examples. We obtain the necessary and sufficient conditions for the distributions to be integrable. We also investigate the necessary and sufficient conditions for these submanifolds to be totally geodesic and study the geometry of foliations determined by the distributions. Finally, we obtain the necessary and sufficient condition for a quasi hemi-slant submanifold to be local product of Riemannian manifold.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.9-13
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• 1992

In this paper, we consider the function related with almost hermitian structure on a copact complex manifold. More precisely, on a 2n-diminsional complex manifold M admitting 2-form .ohm. of rank 2n everywhere, assume that M admits a metric g such that g(JX, JY)=g(X,Y), that is, assume that g defines an hermitian structure on M admitting .ohm. as fundamental 2-form-the 'almost complex structure' J being determined by g and .ohm.:g(X,Y)=.ohm.(X,JY). We consider the function I(g):=.int.$_{M}$ $N^{2}$d $V_{g}$, where N is the norm of Nijenhuis tensor N defined by (J,g). by (J,g).