• East Asian mathematical journal
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• 제35권3호
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• pp.357-363
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• 2019

Let the circle act on a compact almost complex manifold M with a non-empty discrete fixed point set. To each fixed point, there are associated non-zero integers called weights. A positive weight w is called primitive if it cannot be written as the sum of positive weights, other than w itself. In this paper, we show that if every weight is primitive, then the Todd genus Todd(M) of M is positive and there are $Todd(M){\cdot}2^n$ fixed points, where dim M = 2n. This generalizes the result for symplectic semi-free actions by Tolman and Weitsman [8], the result for semi-free actions on almost complex manifolds by the author [6], and the result for certain symplectic actions by Godinho [1].

• Kyungpook Mathematical Journal
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• 제54권2호
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• pp.203-209
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• 2014

We assume that the existence and termination conjecture for flips holds. A complex projective manifold is said to be of almost general type if the intersection number of the canonical divisor with every very general curve is strictly positive. Let f be an algebraic fiber space from X to Y. Then the manifold X is of almost general type if every very general fiber F and the base space Y of f are of almost general type.

• 대한수학회지
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• 제16권1호
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• pp.71-85
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• 1979

• 호남수학학술지
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• 제43권4호
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• pp.701-715
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• 2021

In this paper, we study almost complex Norden Silver manifolds and Kaehler-Norden Silver manifolds. We define adapted connections of first, second and third type to an almost complex Norden Silver manifold and establish the necessary and sufficient conditions for the integrability of almost complex Norden Silver structure. Moreover, we investigate that a complex Norden Silver map is a harmonic map between Kaehler-Norden Silver manifolds.

• 대한수학회지
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• 제33권1호
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• pp.121-136
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• 1996

Met $\tilde{M} = (\tilde{M}, \tilde{J}, <>)$ be an almost Hermitian manifold and M a submanifold of $\tilde{M}$. According to the behavior of the tangent bundle TM with respect to the action of $\tilde{J}$, we have two typical classes of submanifolds. One of them is the class of almost complex submanifolds and another is the class of totally real submanifolds. In 1990, B. Y. Chen [4], [5] introduced the concept of the class of slant submanifolds which involve the above two classes. He used the Wirtinger angle to measure the behavior of TM with respect to the action of $\tilde{J}$.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.83-95
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• 2024

The Quaternionic Dirac operator proves instrumental in tackling various challenges within spectral geometry processing and shape analysis. This work involves the introduction of the quaternionic Dirac operator on a symplectic submanifold of an exact symplectic product manifold. The self adjointness of the symplectic quaternionic Dirac operator is observed. This operator is verified for spin ${\frac{1}{2}}$ particles. It factorizes the Hodge Laplace operator on the symplectic submanifold of an exact symplectic product manifold. For achieving this a new complex structure and an almost quaternionic structure are formulated on this exact symplectic product manifold.

• 대한수학회보
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• 제59권5호
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• pp.1069-1091
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• 2022

We study almost complex metallic Norden manifolds and their adapted connections with respect to an almost complex metallic Norden structure. We study various connections like special connection of the first type, special connection of the second type, Kobayashi-Nomizu metallic Norden type connection, Yano metallic Norden type connection etc., on almost complex metallic Norden manifolds. We establish classifications of almost complex metallic Norden manifolds by using covariant derivative of the almost complex metallic Norden structure and also by using torsion tensor on the canonical connections.

• 대한수학회지
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• 제50권2호
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• pp.231-240
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• 2013

We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and of a round 4-sphere.

• 대한수학회보
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• 제29권1호
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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).

• 대한수학회논문집
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• 제27권2호
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• pp.307-315
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• 2012

We study the geometry of real lightlike hypersurfaces of an inde nite Kaehler manifold $\bar{M}$. We provide new results on such a real lightlike hypersurface $M$ by using the $F$-structure of $M$ induced by the almost complex structure $J$ of $\bar{M}$.