Real hypersurfaces of a complex projective space
Let M be a real hypersurface of a Kähler manifold \((\overline M, J)\) and let \(\xi\) be its unit normal vector field. Then M is a CR submanifold of maximal CR dimension and \(\xi\) is the distinguished normal vector field, used to define the almost contact structure F on M, induced from the almost complex structure J of \(\overline M\). Moreover, since a real hypersurface M of a Kähler manifold \(\overline M\) has two geometric structures: an almost contact structure F and a submanifold structure represented by the shape operator A with respect to \(\xi\), in this section we study the commutativity condition of A and F and we present its geometric meaning.
KeywordsPrincipal Curvature Contact Structure Ahler Manifold Real Hypersurface Shape Operator
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