REAL n-DIMENSIONAL QR-SUBMANIFOLDS OF MAXIMAL QR-DIMENSION IMMERSED IN QP(n+p)/4

Title & Authors
REAL n-DIMENSIONAL QR-SUBMANIFOLDS OF MAXIMAL QR-DIMENSION IMMERSED IN QP(n+p)/4
Kim, Hyang-Sook; Kwon, Jung-Hwan; Pak, Jin-Suk;

Abstract
The purpose of this paper is to study n-dimensional QR-submanifolds of (p-1) QR-dimension immersed in a quaternionic projective space $\small{QP^{(n+p)/4}}$ of constant Q-sectional curvature 4 and especially to determine such submanifolds under the additional condition concerning with shape operator.
Keywords
quaternionic space form;quaternionic projective space;QR-submanifold;QR-dimension;shape operator;
Language
English
Cited by
References
1.
M. Barros, B. Y. Chen, and F. Urbano, Quaternion CR-submanifolds of a quaternion manifolds, Kodai Math. J. 4 (1981), 399–418.

2.
A. Bejancu, Geometry of CR-submanifolds, D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo, 1986.

3.
J. Erbacher, Reduction of the codimension of an isometric immersion, J. Diff. Geom. 5 (1971), 333–340.

4.
S. Ishihara, Quaternion Kaehlerian manifolds, J. Diff. Geom. 9 (1974), 483–500.

5.
S. Ishihara and M. Konishi, Differential geometry of fibred spaces, Publication of the study group of geometry. Vol. 8, Tokyo, 1973.

6.
J.-H. Kwon and J. S. Pak, QR-submanifolds of (p-1) QR-dimension in a quaternionic projective space QP\$QP^{{n+p)/4}\$, Acta Math. Hungarica 86 (2000), 89–116.

7.
J.-H. Kwon and J. S. Pak, Codimension reduction for real submanifolds of quaternionic projective space, J. Korean Math. Soc. 36 (1999), no. 1, 109–123.

8.
J.-H. Kwon and J. S. Pak, Scalar curvature of QR-submanifolds immersed in a quaternionic projective space, Saitama Math. J. 17 (1999), 47–57.

9.
J.-H. Kwon and J. S. Pak, n-dimensional CR-submanifolds of (n-1) CR- dimension immersed in a complex space form, Far East J. of Math. Sci. Special Volume, part III (1999), 347–360.

10.
H. B. Lawson, Jr.Rigidity theorems in rank-1 symmetric spaces, J. Diff. Geom. 4 (1970), 349–357.

11.
A. Martinez and J. D. Perez, Real hypersurfaces in quaternionic projective space, Ann. Mat. Pura Appl. 145 (1986), 355–384.

12.
J. S. Pak, Real hypersurfaces in quaternionic Kaehlerian manifolds with constant Q-sectional curvature, Kodai Math. Sem. Rep. 29 (1977), 22–61.