Examples of foliations with foliated geometric structures

Luis A. Cordero and Robert Wolak

Vol. 142 (1990), No. 2, 265–276

DOI: 10.2140/pjm.1990.142.265

Abstract

We present examples of foliated compact nilmanifolds, whose foliations are neither simple nor given by suspensions, admitting various foliated geometric structures. For example, we construct foliations which are:

1. transversely symplectic but not transversely Kähler,
2. transversely symplectic but not transversely holomorphic,
3. transversely Sasakian but not transversely cosymplectic.

Mathematical Subject Classification 2000

Primary: 53C12

Secondary: 57R30

Milestones

Received: 9 May 1988

Revised: 13 March 1989

Published: 1 April 1990