Abstract
In analogy with the Gauss mapping for a subvariety in the complex projective space, the Gauss mapping for a subvariety in a complex hyperbolic space form can be defined as a map from the smooth locus of the subvariety to the quotient of a suitable domain in the Grassmannian. For complex hyperbolic space forms of finite volume, it is proved that the Gauss mapping is degenerate if and only if the subvariety is totally geodesic.
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