Vol. 111, No. 1, 1984

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Some examples of Riemannian almost-product manifolds

Vicente Miquel Molina

Vol. 111 (1984), No. 1, 163–178

Foliations with bundle-like metrics, conformal, minimal and totally geodesic foliations and minimal and geodesic plane fields have been subject to recent study. A. M. Naveira has fitted all these classes into a general scheme and has gotten thirty six classes of riemannian almost-product manifolds. In this paper we give strict examples of these classes, showing that none of them is vacuous, and that the inclusion relations among them are strict. The basic riemannian manifolds for the construction of these examples are submanifolds of Cn+1 and Hn+1 (C = complex field, H = quaternion field), and we use the canonical complex structures on these vector spaces. Perhaps the most interesting examples are those of minimal foliations which are not totally geodesic foliations.

Mathematical Subject Classification 2000
Primary: 53C15
Secondary: 53C10
Received: 16 February 1982
Published: 1 March 1984
Vicente Miquel Molina