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A characterization of seven compact Kähler submanifolds by holomorphic pinching. (English) Zbl 0589.53065
Let \(P_ m(C)\) be an m-dimensional complex projective space with the Fubini-Study metric of constant holomorphic sectional curvature 1, and let M be an n-dimensional compact Kähler submanifold immersed in \(P_ m(C)\). By applying an ingenious but simple method, the author proves that if the holomorphic sectional curvature of M is \(\geq\), then M is a totally geodesic \(P_ n(C)\), Veronese \(P_ n(C)\), a Segre submanifold \(P_ k(C)\), \(P_{n-k}(C)\) or an Hermitian symmetric space of rank 2 with parallel second fundamental form.
Reviewer: K.Ogiue

MSC:
53C55 Global differential geometry of Hermitian and Kählerian manifolds
53C40 Global submanifolds
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