On a -dimensional Einstein Kaehler submanifold of a complex space form

Author:
Yoshio Matsuyama

Journal:
Proc. Amer. Math. Soc. **95** (1985), 595-603

MSC:
Primary 53C25; Secondary 53C40

DOI:
https://doi.org/10.1090/S0002-9939-1985-0810170-0

MathSciNet review:
810170

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Abstract: In this paper we consider when a Kaehler submanifold of a complex space form is Einstein with respect to the induced metric. Then we shall show that (1) a -dimensional complete Kaehler submanifold of a -dimensional complex projective space is Einstein if and only if is holomorphically isometric to which is totally geodesic in or a hyperquadric in which is totally geodesic in , and that (2) if is a -dimensional Einstein Kaehler submanifold of a -dimensional complex space form of nonpositive constant holomorphic sectional curvature , then is totally geodesic.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0810170-0

Keywords:
Einstein Kaehler submanifolds,
complex space forms,
second fundamental forms

Article copyright:
© Copyright 1985
American Mathematical Society