# New examples of compact cosymplectic solvmanifolds

J. C. Marrero; E. Padrón-Fernández

Archivum Mathematicum (1998)

- Volume: 034, Issue: 3, page 337-345
- ISSN: 0044-8753

## Access Full Article

top## Abstract

top## How to cite

topMarrero, J. C., and Padrón-Fernández, E.. "New examples of compact cosymplectic solvmanifolds." Archivum Mathematicum 034.3 (1998): 337-345. <http://eudml.org/doc/248176>.

@article{Marrero1998,

abstract = {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 product of the $(2m+1)$-dimensional real torus and the $r$-dimensional complex projective space, with $m,r\ge 0$ 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 $S^1.$},

author = {Marrero, J. C., Padrón-Fernández, E.},

journal = {Archivum Mathematicum},

keywords = {cosymplectic manifolds; solvmanifolds; Kähler manifolds; suspensions; flat Riemannian manifolds; cosymplectic manifold; solvmanifold; Kähler manifold; suspension; flat Riemannian manifold},

language = {eng},

number = {3},

pages = {337-345},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {New examples of compact cosymplectic solvmanifolds},

url = {http://eudml.org/doc/248176},

volume = {034},

year = {1998},

}

TY - JOUR

AU - Marrero, J. C.

AU - Padrón-Fernández, E.

TI - New examples of compact cosymplectic solvmanifolds

JO - Archivum Mathematicum

PY - 1998

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 034

IS - 3

SP - 337

EP - 345

AB - 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 product of the $(2m+1)$-dimensional real torus and the $r$-dimensional complex projective space, with $m,r\ge 0$ 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 $S^1.$

LA - eng

KW - cosymplectic manifolds; solvmanifolds; Kähler manifolds; suspensions; flat Riemannian manifolds; cosymplectic manifold; solvmanifold; Kähler manifold; suspension; flat Riemannian manifold

UR - http://eudml.org/doc/248176

ER -

## References

top- Blair D. E., Contact manifolds in Riemannian geometry, Lecture Notes in Math., 509, Springer-Verlag, Berlin, (1976). (1976) Zbl0319.53026MR0467588
- Blair D. E., Goldberg S. I., Topology of almost contact manifolds, J. Diff. Geometry, 1, 347-354 (1967). (1967) Zbl0163.43902MR0226539
- Chinea D., León M. de, Marrero J. C., Topology of cosymplectic manifolds, J. Math. Pures Appl., 72, 567-591 (1993). (1993) Zbl0845.53025MR1249410
- Hector G., Hirsch U., Introduction to the Geometry of Foliations. Part A, Aspects of Math., Friedr. Vieweg and Sohn, (1981). (1981) Zbl0486.57002MR0639738
- 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). (1997) Zbl0897.53026MR1620868
- Wolf J. A., Spaces of constant curvature, 5nd ed., Publish or Perish, Inc., Wilmington, Delaware, (1984). (1984) Zbl0556.53033MR0928600

## NotesEmbed ?

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