EXAMPLES OF TRANSVERSALLY COMPLEX SUBMANIFOLDS OF THE ASSOCIATIVE GRASSMANN MANIFOLD

被引：3

作者：

Enoyoshi, Kanako ^{[1
]}

Tsukada, Kazumi ^{[2
]}

机构：

[1] Ochanomizu Univ, Grad Sch Humanities & Sci, Bunkyo Ku, 2-1-1 Otsuka, Tokyo 1128610, Japan

[2] Ochanomizu Univ, Dept Math, Bunkyo Ku, 2-1-1 Otsuka, Tokyo 1128610, Japan

来源：

TSUKUBA JOURNAL OF MATHEMATICS | 2019年 / 43卷 / 01期

关键词：

the associative Grassmann manifold; a quaternionic Kahler manifold; transversally complex submanifolds; totally complex submanifolds; KAHLER SUBMANIFOLDS;

D O I：

10.21099/tkbjm/1571968819

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Grassmann manifold of associative subspaces in the space of imaginary octonions, which we call the associative Grassmann manifold. It is known that the associative Grassmann manifold is an eight-dimensional compact symmetric quaternionic Kahler manifold. We construct interesting examples of four-dimensional complex submanifolds of the associative Grassmann manifold.

引用

页码：23 / 36

页数：14

共 17 条

[1] A twistor construction of Kahler submanifolds of a quaternionic Kahler manifold [J].

Alekseevsky, D. V. ;

Marchiafava, S. .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2005, 184 (01) :53-74

[2]

Alekseevsky DV, 2001, OSAKA J MATH, V38, P869

[3] Quaternionic structures on a manifold and subordinated structures. [J].

Alekseevsky, DV ;

Marchiafava, S .

ANNALI DI MATEMATICA PURA ED APPLICATA, 1996, 171 :205-273

[4] Maximal totally complex submanifolds of HPn: homogeneity and normal holonomy [J].

Bedulli, Lucio ;

Gori, Anna ;

Podesta, Fabio .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2009, 41 :1029-1040

[5]

BURSTALL F.E., 2002, SPRINGER LECT NOTES, V1772

[6]

Funabashi S., 1979, Kodai Math. J., V2, P314

[7] CALIBRATED GEOMETRIES [J].

HARVEY, R ;

LAWSON, HB .

ACTA MATHEMATICA, 1982, 148 :47-157

[8]

Ishihara S., 1974, J DIFFER GEOM, V9, P483

[9] Hopf hypersurfaces in complex projective space and half-dimensional totally complex submanifolds in complex 2-plane Grassmannian I [J].

Kimura, Makoto .

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2014, 35 :156-163

[10]

Klein S, 2010, OSAKA J MATH, V47, P1077

← 1 2 →