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TRANSVERSE KILLING FORMS ON A KAHLER FOLIATION
정승달,정민주 대한수학회 2012 대한수학회보 Vol.49 No.3
On a closed, connected Riemannian manifold with a K$\ddot{a}$ahler foliation $\mathcal{F}$ of codimension $q$, any transverse Killing $r$-form ($2{\leq}r{\leq}q$) is parallel.
The properties of Riemannian foliations admitting transversal conformal fields
정승달,이금란 대한수학회 2018 대한수학회보 Vol.55 No.4
Let $(M,\mathcal F)$ be a closed, oriented Riemannian manifold of a foliation $\mathcal F$ with a nonisometric transversal conformal field. Then $(M,\mathcal F)$ is transversally isometric to the sphere under some transversal concircular curvature conditions.
정승달,문영봉 대한수학회 2005 대한수학회지 Vol.42 No.6
We study the properties of the transversal Killing and twistorspinors for a Riemannian foliation with a transverse spinstructure. And we investigate the relations between them. As anapplication, we give a new lower bound for the eigenvalues of thebasic Dirac operator by using the transversal twistor operator.
TRANSVERSE KILLING FORMS ON COMPLETE FOLIATED RIEMANNIAN MANIFOLDS
정승달 호남수학회 2014 호남수학학술지 Vol.36 No.4
In this article, we study the transverse Killing forms with finite global norms on complete foliated Riemannian manifolds.
CLIFFORD L²-COHOMOLOGY ON THE COMPLETE KAHLER MANIFOLDS
JUNG, SEOUNG DAL,PAK, JIN SUK 濟州大學校 基礎科學硏究所 1997 基礎科學硏究 Vol.10 No.1
In the study of a manifold M, the exterior algebra A*M plays an important role. In Fact, the de Rham cohomology theory gives many informations of a manifold. Another important object in the study of a manifold is its Cliflord algebra Cl(M), generated by the tangent space. It carries an intrinsic first order elliptic operator D, the Dirac operator. Tehere is a canonical vector (but not algebra) bundle isomorphism ∧^*(M)→Cl(M). In ∧^*(M), the Dirac opcrator D is D=d+δ, where d is the exterior differential and δ is the adjoint of d. Therefore many results of the Clifford theory yield the results of the de Rham theory ([8]). Moreover the calculus of the pair Cl(M), D carries over formally to bundles of modules over Cl(M).
SOME VANISHING THEOREMS ON KAHLER FOLIATIONS
PAK, JIN SUK,JUNG, SEOUNG DAL 濟州大學校 基礎科學硏究所 1996 基礎科學硏究 Vol.9 No.1
We shall prove some vanishing theorems for the transversal Dirac operators on Kahler foliations