Browse > Article
http://dx.doi.org/10.4134/BKMS.2014.51.5.1375

CODIMENSION REDUCTION FOR SUBMANIFOLDS OF UNIT (4m+3)-SPHERE AND ITS APPLICATIONS  

Kim, Hyang Sook (Department of Applied Mathematics Institute of Basic Science Inje University)
Pak, Jin Suk (Kyungpook National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.51, no.5, 2014 , pp. 1375-1397 More about this Journal
Abstract
In this paper we establish codimension reduction theorem for submanifolds of a (4m+3)-dimensional unit sphere $S^{4m+3}$ with Sasakian 3-structure and apply it to submanifolds of a quaternionic projective space.
Keywords
codimension reduction; unit (4m + 3)-sphere; Sasakian 3-structure; normal connection; quaternionic projective space; L-flat; mean curvature vector; totally geodesic;
Citations & Related Records
연도 인용수 순위
  • Reference
1 S. Ishihara and M. Konish, Differential Geometry of Fibred Spaces, Study Group of Differential Geometry, Tokyo, 1973.
2 T. Kashiwada, A note on a Riemannian space with Sasakian 3-structure, Natur. Sci. Rep. Ochanomizu Univ. 22 (1971), 1-2.
3 S. Kawamoto, Codimension reduction for real submanifolds of a complex hyperbolic space, Rev. Mat. Univ. Complut. Madrid 7 (1994), no. 1, 119-128.
4 H. S. Kim and J. S. Pak, Codimension reduction for real submanifolds of quaternionic hyperbolic space, Acta Math. Hungar. 121 (2008), no. 1-2, 21-33.   DOI
5 Y. Y. Kuo, On almost contact 3-structure, Tohoku Math. J. 22 (1970), 325-332.   DOI
6 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.   과학기술학회마을
7 H. B. Lawson, Jr., Rigidity theorems in rank-1 symmetric spaces, J. Differential Geom-etry 4 (1970), 349-357.   DOI
8 M. Okumura, Reducing the codimension of a submanifold of a complex projective space, Geom. Dedicata 13 (1982), no. 3, 277-289.
9 M. Okumura, Codimension reduction problem for real submanifold of complex projective space, Differential geometry and its applications (Eger, 1989), 573-585, Colloq. Math. Soc. Janos Bolyai, 56, North-Holland, Amsterdam, 1992.
10 J. S. Pak, Real hypersurfaces in quaternionic Kaehlerian manifolds with constant Q-sectional curvature, Kodai Math. Sem. Rep. 29 (1977), no. 1-2, 22-61.   DOI
11 Y. Shibuya, Real submanifolds in a quaternionic projective space, Kodai Math. J. 1 (1978), no. 3, 421-439.   DOI
12 S. Tachibana and W. N. Yu, On a Riemannian space admitting more than one Sasakian structures, Tohoku Math. J. 22 (1970), 536-540.   DOI
13 C. B. Allendoerfer, Rigidity for spaces of class greater than one, Amer. J. Math. Soc. 61 (1939), 633-644.   DOI   ScienceOn
14 T. E. Cecil, Geometric applications of critical point theory to submanifolds of complex projective space, Nagoya Math J. 55 (1974), 5-31.   DOI
15 S. Ishihara, Quaternion Kaehlerian manifolds, J. Differential Geometry 9 (1974), 483-500.   DOI
16 B. Y. Chen, Geometry of Submanifolds, Marcel Dekker Inc., New York, 1973.
17 J. Erbacher, Reduction of the codimension of an isometric immersion, J. Differential Geometry 5 (1971), 333-340.   DOI