On the normality of an almost contact 3 -structure on Q R -submanifolds

Shoichi Funabashi; Jin Suk Pak; Yang Jae Shin

Czechoslovak Mathematical Journal (2003)

  • Volume: 53, Issue: 3, page 571-589
  • ISSN: 0011-4642

Abstract

top
We study n -dimensional Q R -submanifolds of Q R -dimension ( p - 1 ) immersed in a quaternionic space form Q P ( n + p ) / 4 ( c ) , c ≧ 0 , and, in particular, determine such submanifolds with the induced normal almost contact 3 -structure.

How to cite

top

Funabashi, Shoichi, Pak, Jin Suk, and Shin, Yang Jae. "On the normality of an almost contact $3$-structure on $QR$-submanifolds." Czechoslovak Mathematical Journal 53.3 (2003): 571-589. <http://eudml.org/doc/30800>.

@article{Funabashi2003,
abstract = {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.},
author = {Funabashi, Shoichi, Pak, Jin Suk, Shin, Yang Jae},
journal = {Czechoslovak Mathematical Journal},
keywords = {quaternionic projective space; quaternionic number space; $QR$-submanifold; normal almost contact $3$-structure; quaternionic projective space; quaternionic number space; -submanifold; normal almost contact 3-structure},
language = {eng},
number = {3},
pages = {571-589},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the normality of an almost contact $3$-structure on $QR$-submanifolds},
url = {http://eudml.org/doc/30800},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Funabashi, Shoichi
AU - Pak, Jin Suk
AU - Shin, Yang Jae
TI - On the normality of an almost contact $3$-structure on $QR$-submanifolds
JO - Czechoslovak Mathematical Journal
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 3
SP - 571
EP - 589
AB - 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.
LA - eng
KW - quaternionic projective space; quaternionic number space; $QR$-submanifold; normal almost contact $3$-structure; quaternionic projective space; quaternionic number space; -submanifold; normal almost contact 3-structure
UR - http://eudml.org/doc/30800
ER -

References

top
  1. Quaternion C R -submanifolds of a quaternion manifold, Kodai Math.  J. 4 (1981), 399–418. (1981) MR0641361
  2. Geometry of C R -submanifolds, D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo, 1986. (1986) Zbl0605.53001MR0861408
  3. Geometry of Submanifolds, Marcel Dekker Inc., New York, 1973. (1973) Zbl0262.53036MR0353212
  4. 10.4310/jdg/1214429997, J.  Differential Geom. 5 (1971), 333–340. (1971) MR0288701DOI10.4310/jdg/1214429997
  5. 10.4310/jdg/1214432544, J.  Differential Geom. 9 (1974), 483–500. (1974) Zbl0297.53014MR0348687DOI10.4310/jdg/1214432544
  6. Differential geometry of fibred spaces, Publication of the Study Group of Geometry, Vol.  8, Institute of Mathematics, Yoshida College, Tokyo, 1973. (1973) MR0405275
  7. The trace decomposition problem, Beiträge Algebra Geom.; Contrib. Alg. Geom. 36 (1995), 303–315. (1995) Zbl0839.15024MR1358429
  8. On almost contact 3 -structure, Tohoku Math.  J. 22 (1970), 235–332. (1970) Zbl0205.25801MR0278225
  9. 10.1023/A:1006795518714, Acta Math. Hungar. 86 (2000), 89–116. (2000) MR1728592DOI10.1023/A:1006795518714
  10. Scalar curvature of Q R -submanifolds immersed in a quaternionic projective space, Saitama Math.  J 17 (1999), 47–57. (1999) MR1740246
  11. On n -dimensional Q R -submanifolds of ( p - 1 ) Q R -dimension in a quaternionic space form, Preprint. 
  12. A class of normal almost contact C R -submanifolds in  C q , Rend. Sem. Mat. Univ. Pol. Torino 52 (1994), 359–369. (1994) MR1345606
  13. 10.2996/kmj/1138833571, Kodai Math. Sem. Rep. 29 (1977), 22–61. (1977) Zbl0424.53012MR0461384DOI10.2996/kmj/1138833571
  14. 10.2748/tmj/1178241375, Tohoku Math.  J. 25 (1973), 167–175. (1973) MR0336644DOI10.2748/tmj/1178241375

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.