Harmonic 1-Forms on Compact f-Manifolds

We consider a Riemannian manifold with a compatible f-structure which admits a parallelizable kernel. With some additional integrability conditions it is called -manifold. This class of manifolds is a natural generalization of the Sasakian manifolds. We study properties of harmonic 1-forms on such a manifold and deduce some topological properties. Research supported by the Italian MIUR 60% and GNSAGA. Professor J.J. Konderak died just during the preparation of this paper. His contribution has been substantial. Note of the Editor-in-Chief. Professor Jerzy J. Konderak passed away on September 14, 2005, at the age of 49. Born on February 12, 1956, in Krakow, Poland, he received his Ph.D. in 1986 from the Jagiellonian University of Krakow. Since 2003 he was associated professor of Mathematics at the Faculty of Sciences of the University of Bari. The main area of his scientific interests was Differential Geometry. Professor Konderak was a very gifted researcher and was appreciated by students and colleagues for his passion and devotion to Mathematics and its teaching. All the colleagues of the Department of Mathematics of the University of Bari will remember him not only as a clever mathematician but also as a men of rare quality.