Jin Suk Pak

QR-SUBMANIFOLDS OF MAXIMAL QR-DIMENSION IN QUATERNIONIC PROJECTIVE SPACE

The purpose of this paper is to study n-dimensional QR-submanifolds of maximal QR-dimension isometrically immersed in a quaternionic projective space and to give su-cient conditions in order for such a submanifold to be a tube over a quaternionic invariant submanifold.

CERTAIN CONTACT CR-SUBMANIFOLDS OF AN ODD-DIMENSIONAL UNIT SPHERE

We study an (n+1)(n ≥ 3)-dimensional contact CR-submanifold of (n−1) contact CR-dimension in a (2m+1)-unit sphere S2m+1, and to determine such submanifolds under conditions concerning the second fundamental form and the induced almost contact structure.

Application of an integral formula to CR-submanifolds of complex hyperbolic space

The purpose of this paper is to study n-dimensional compact CR-submanifolds of complex hyperbolic space CH(n

On the spectral geometry for the Jacobi operators of harmonic maps into a quaternionic projective space

We characterize both invariant and totally real immersions into the quaternionic projective space by the spectra of the Jacobi operator. Also, we study spectral characterization of harmonic submersions when the target manifold is the quaternionic projective space.

SCALAR CURVATURE OF CONTACT CR-SUBMANIFOLDS IN AN ODD-DIMENSIONAL UNIT SPHERE

In this paper we derive an integral formula on an (n + 1)-dimensional, compact, minimal contact CR-submanifold M of (n - 1) contact CR-dimension immersed in a unit (2m+1)-sphere . Using this integral formula, we give a sufficient condition concerning with the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.

CERTAIN CLASS OF CONTACT CR-SUBMANIFOLDS OF A SASAKIAN SPACE FORM

Abstract. In this paper we investigate (n+1)(n ≥ 3)-dimensional con-tact CR-submanifolds M of (n−1) contact CR-dimension in a completesimply connected Sasakian space form of constant φ-holomorphic sec-tional curvature c 6= −3 which satisfy the condition h(FX,Y )+h(X,FY )= 0 for any vector fields X,Y tangent to M, where h and F denote thesecond fundamental form and a skew-symmetric endomorphism (definedby (2.3)) acting on tangent space of M, respectively. 1. IntroductionLet S 2m+1 be a (2m + 1)-unit sphere in the complex (m + 1)-space C m+1 ,i.e.,S 2m+1 := {(z 1 ,...,z m+1 ) ∈ C m+1 | m X +1j=1 |z j | 2 = 1}.For any point z ∈ S 2m+1 we put ξ = Jz, where J denotes the complex structureof C m+1 . Denoting by π the orthogonal projection : T z C m+1 → T z S 2m+1 andputting φ = π◦J, we can see that the set (φ,ξ,η,g) defines a Sasakian structureon S 2m+1 , where g is the standard metric on S 2m+1 induced from that of C m+1 and η is a 1-form dual to ξ. Hence S 2m+1 can be considered as a Sasakianmanifold of constant curvature 1 (cf. [2, 4, 5, 6, 7, 8, 9]).Let M be an (n+1)-dimensional submanifold tangent to the structure vectorfield ξ of S

-Submanifolds of -Dimension in a Quaternionic Projective Space under Some Curvature Conditions

The purpose of this paper is to study n-dimensional -submanifolds of -dimension in a quaternionic projective space and especially to determine such submanifolds under some curvature conditions.

CERTAIN CLASS OF QR-SUBMANIFOLDS OF MAXIMAL QR-DIMENSION IN QUATERNIONIC SPACE FORM

In this paper we determine certain class of -dimensional QR-submanifolds of maximal QR-dimension isometrically immersed in a quaternionic space form, that is, a quaternionic Khler manifold of constant Q-sectional curvature under the conditions (3.1) concerning with the second fundamental form and the induced almost contact 3-structure.

SCALAR CURVATURE OF CONTACT THREE CR-SUBMANIFOLDS IN A UNIT (4m + 3)-SPHERE

In this paper we derive an integral formula on an ( n + 3)- dimensional, compact, minimal contact three CR-submanifold M of ( p

CONTACT THREE CR-SUBMANIFOLDS OF A (4m + 3)-DIMENSIONAL UNIT SPHERE

We study (n＋3)-dimensional contact three CR submanifolds of a Riemannian manifold with Sasakian three structure and investigate some characterizations of (a) (b) (＋ =1, 4(r ＋ s) = n - 3) as a contact three CR sub manifold of a (4m＋3)-dimensional unit sphere.