Certain condition on the second fundamental form of CR submanifolds of maximal CR dimension of complex Euclidean space

Author: Djorić Mirjana  

Publisher: Springer Publishing Company

ISSN: 0232-704X

Source: Annals of Global Analysis and Geometry, Vol.30, Iss.4, 2006-11, pp. : 383-396

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Abstract

We treat m</i>-dimensional real submanifolds m</i> of complex space forms m</i> when the maximal holomorphic tangent subspace is (m</i>−1)-dimensional. On these manifolds there exists an almost contact structure F</i> which is naturally induced from the ambient space and in this paper we study the condition h</i>(FX</i>,Y</i>)−h</i>(X</i>,FY</i>) = g</i>(FX</i>,Y</i>), ∈ T</i>⊥(m</i>), on the structure F</i> and on the second fundamental form h</i> of these submanifolds. Especially when the ambient space m</i> is a complex Euclidean space, we obtain a complete classification of submanifolds m</i> which satisfy these conditions.