| Title:
|
Contact manifolds, harmonic curvature tensor and $(k,\mu )$-nullity distribution (English) |
| Author:
|
Papantoniou, Basil J. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
323-334 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we give first a classification of contact Riemannian manifolds with harmonic curvature tensor under the condition that the characteristic vector field $\xi $ belongs to the $(k,\mu )$-nullity distribution. Next it is shown that the dimension of the $(k,\mu )$-nullity distribution is equal to one and therefore is spanned by the characteristic vector field $\xi $. (English) |
| Keyword:
|
contact Riemannian manifold |
| Keyword:
|
harmonic curvature |
| Keyword:
|
$D$-homothetic deformation |
| MSC:
|
53C05 |
| MSC:
|
53C15 |
| MSC:
|
53C20 |
| MSC:
|
53C21 |
| MSC:
|
53C25 |
| idZBL:
|
Zbl 0782.53024 |
| idMR:
|
MR1241740 |
| . |
| Date available:
|
2009-01-08T18:03:40Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118584 |
| . |
| Reference:
|
[1] Baikoussis C., Koufogiorgos T.: On a type of contact manifolds.to appear in Journal of Geometry. MR 1205692 |
| Reference:
|
[2] Blair D.E.: Contact manifolds in Riemannian geometry.Lecture Notes in Mathematics 509, Springer-Verlag, Berlin, 1979. Zbl 0319.53026, MR 0467588 |
| Reference:
|
[3] Blair D.E.: Two remarks on contact metric structures.Tôhoku Math. J. 29 (1977), 319-324. Zbl 0376.53021, MR 0464108 |
| Reference:
|
[4] Blair D.E., Koufogiorgos T., Papantoniou B.J.: Contact metric manifolds with characteristic vector field satisfying $R(X,Y)\xi =k(\eta (Y)X-\eta (X)Y)+\mu (\eta (Y)hX-\eta (X)hY)$.submitted. |
| Reference:
|
[5] Deng S.R.: Variational problems on contact manifolds.Thesis, Michigan State University, 1991. |
| Reference:
|
[6] Koufogiorgos T.: Contact metric manifolds.to appear in Annals of Global Analysis and Geometry. MR 1201408 |
| Reference:
|
[7] Tanno S.: Ricci curvatures of contact Riemannian manifolds.Tôhoku Math J. 40 (1988), 441-448. Zbl 0655.53035, MR 0957055 |
| . |
