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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

CR submanifolds of a Kaehler manifold. II


Author: Aurel Bejancu
Journal: Trans. Amer. Math. Soc. 250 (1979), 333-345
MSC: Primary 53C40; Secondary 32C05
MathSciNet review: 530059
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Abstract: The differential geometry of CR submanifolds of a Kaehler manifold is studied. Theorems on parallel normal sections and on a special type of flatness of the normal connection on a CR submanifold are obtained. Also, the nonexistence of totally umbilical proper CR submanifolds in an elliptic or hyperbolic complex space is proven.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0530059-6
PII: S 0002-9947(1979)0530059-6
Keywords: CR submanifold, mixed totally geodesic CR submanifold, foliate CR submanifold, totally umbilical CR submanifold, $ \left( {D,\,\mu } \right)$-flat normal connection
Article copyright: © Copyright 1979 American Mathematical Society