| Title:
|
On the normality of an almost contact $3$-structure on $QR$-submanifolds (English) |
| Author:
|
Funabashi, S. |
| Author:
|
Pak, J. S. |
| Author:
|
Shin, Y. J. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
571-589 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study $n$-dimensional $QR$-submanifolds of $QR$-dimension $(p-1)$ immersed in a quaternionic space form $QP^{(n+p)/4}(c)$, $c\geqq 0$, and, in particular, determine such submanifolds with the induced normal almost contact $3$-structure. (English) |
| Keyword:
|
quaternionic projective space |
| Keyword:
|
quaternionic number space |
| Keyword:
|
$QR$-submanifold |
| Keyword:
|
normal almost contact $3$-structure |
| MSC:
|
53C40 |
| MSC:
|
53D15 |
| idZBL:
|
Zbl 1080.53050 |
| idMR:
|
MR2000054 |
| . |
| Date available:
|
2009-09-24T11:04:36Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127824 |
| . |
| Reference:
|
[1] M. Barros, B. Y. Chen and F. Urbano: Quaternion $CR$-submanifolds of a quaternion manifold.Kodai Math. J. 4 (1981), 399–418. MR 0641361 |
| Reference:
|
[2] A. Bejancu: Geometry of $CR$-submanifolds.D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo, 1986. Zbl 0605.53001, MR 0861408 |
| Reference:
|
[3] B. Y. Chen: Geometry of Submanifolds.Marcel Dekker Inc., New York, 1973. Zbl 0262.53036, MR 0353212 |
| Reference:
|
[4] J. Erbacher: Reduction of the codimension of anisometric immersion.J. Differential Geom. 5 (1971), 333–340. MR 0288701, 10.4310/jdg/1214429997 |
| Reference:
|
[5] S. Ishihara: Quaternion Kaehlerian manifolds.J. Differential Geom. 9 (1974), 483–500. Zbl 0297.53014, MR 0348687, 10.4310/jdg/1214432544 |
| Reference:
|
[6] S. Ishihara and M. Konishi: Differential geometry of fibred spaces.Publication of the Study Group of Geometry, Vol. 8, Institute of Mathematics, Yoshida College, Tokyo, 1973. MR 0405275 |
| Reference:
|
[7] D. Krupka: The trace decomposition problem.Beiträge Algebra Geom.; Contrib. Alg. Geom. 36 (1995), 303–315. Zbl 0839.15024, MR 1358429 |
| Reference:
|
[8] Y. Y. Kuo: On almost contact $3$-structure.Tohoku Math. J. 22 (1970), 235–332. Zbl 0205.25801, MR 0278225 |
| Reference:
|
[9] J.-H. Kwon and J. S. Pak: $QR$-submanifolds of $(p-1)$ $QR$-dimension in a quaternionic projective space $QP^{(n+p)/4}$.Acta Math. Hungar. 86 (2000), 89–116. MR 1728592, 10.1023/A:1006795518714 |
| Reference:
|
[10] 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. MR 1740246 |
| Reference:
|
[11] J.-H. Kwon and J. S. Pak: On $n$-dimensional $QR$-submanifolds of $(p-1)$ $QR$-dimension in a quaternionic space form.Preprint. |
| Reference:
|
[12] M. Okumura and L. Vanhecke: A class of normal almost contact $CR$-submanifolds in $C^q$.Rend. Sem. Mat. Univ. Pol. Torino 52 (1994), 359–369. MR 1345606 |
| Reference:
|
[13] J. S. Pak: Real hypersurfaces in quaternionic Kaehlerian manifolds with constant $Q$-sectional curvature.Kodai Math. Sem. Rep. 29 (1977), 22–61. Zbl 0424.53012, MR 0461384, 10.2996/kmj/1138833571 |
| Reference:
|
[14] K. Yano, S. Ishihara and M. Konishi: Normality of almost contact $3$-structure.Tohoku Math. J. 25 (1973), 167–175. MR 0336644, 10.2748/tmj/1178241375 |
| . |
