| Title:
|
New examples of compact cosymplectic solvmanifolds (English) |
| Author:
|
Marrero, J. C. |
| Author:
|
Padron, E. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
34 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
337-345 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we present new examples of $(2n+1)$-dimensional compact cosymplectic manifolds which are not topologically equivalent to the canonical examples, i.e., to the pro\-duct of the $(2m+1)$-dimensional real torus and the $r$-dimensional complex projective space, with $m,r\geq 0$ and $m+r=n.$ These new examples are compact solvmanifolds and they are constructed as suspensions with fibre the $2n$-dimensional real torus. In the particular case $n=1,$ using the examples obtained, we conclude that a $3$-dimensional compact flat orientable Riemannian manifold with non-zero first Betti number admits a cosymplectic structure. Furthermore, if the first Betti number is equal to $1$ then such a manifold is not topologically equivalent to the global product of a compact Kähler manifold with the circle $S^1.$ (English) |
| Keyword:
|
cosymplectic manifolds |
| Keyword:
|
solvmanifolds |
| Keyword:
|
Kähler manifolds |
| Keyword:
|
suspensions |
| Keyword:
|
flat Riemannian manifolds |
| MSC:
|
53C15 |
| MSC:
|
53C55 |
| MSC:
|
53D35 |
| idZBL:
|
Zbl 0968.53054 |
| idMR:
|
MR1662115 |
| . |
| Date available:
|
2009-02-17T10:14:17Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107660 |
| . |
| Reference:
|
[1] Blair D. E.: Contact manifolds in Riemannian geometry.Lecture Notes in Math., 509, Springer-Verlag, Berlin, (1976). Zbl 0319.53026, MR 0467588 |
| Reference:
|
[2] Blair D. E., Goldberg S. I.: Topology of almost contact manifolds.J. Diff. Geometry, 1, 347-354 (1967). Zbl 0163.43902, MR 0226539 |
| Reference:
|
[3] Chinea D., León M. de, Marrero J. C.: Topology of cosymplectic manifolds.J. Math. Pures Appl., 72, 567-591 (1993). Zbl 0845.53025, MR 1249410 |
| Reference:
|
[4] Hector G., Hirsch U.: Introduction to the Geometry of Foliations. Part A.Aspects of Math., Friedr. Vieweg and Sohn, (1981). Zbl 0486.57002, MR 0639738 |
| Reference:
|
[5] León M. de, Marrero J. C.: Compact cosymplectic manifolds with transversally positive definite Ricci tensor.Rendiconti di Matematica, Serie VII, 17 Roma, 607-624 (1997). Zbl 0897.53026, MR 1620868 |
| Reference:
|
[6] Wolf J. A.: Spaces of constant curvature.5nd ed., Publish or Perish, Inc., Wilmington, Delaware, (1984). Zbl 0556.53033, MR 0928600 |
| . |
