Vol. 27, No. 2, 1968

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Totally geodesic hypersurfaces of Kaehler manifolds

Samuel Irving Goldberg

Vol. 27 (1968), No. 2, 275–281

It is known that a C orientable totally umbilical hypersurface P with nonzero mean curvature of a Kaehler manifold M is a normal contact manifold. Moreover, if M = Cn with the flat Kaehler metric, P can be realized as a normal contact metric manifold of positive constant curvature. It is the main purpose of this paper to obtain corresponding results for cosymplectic manifolds.

The direct product of two normal almost contact manifolds can be endowed with a complex structure. For cosymplectic manifolds more is obtained. Indeed, the direct product of two cosymplectic manifolds can be given a Kaehlerian structure. This is particularly true of orientable totally geodesic hypersurfaces of a Kaehler manifold.

Mathematical Subject Classification
Primary: 53.74
Received: 20 December 1967
Published: 1 November 1968
Samuel Irving Goldberg