Totally real submanifolds in

satisfying Chen's equality

Authors:
Franki Dillen and Luc Vrancken

Journal:
Trans. Amer. Math. Soc. **348** (1996), 1633-1646

MSC (1991):
Primary 53B25; Secondary 53A10, 53B35, 53C25, 53C42

MathSciNet review:
1355070

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Abstract: In this paper, we study 3-dimensional totally real submanifolds of . If this submanifold is contained in some 5-dimensional totally geodesic , then we classify such submanifolds in terms of complex curves in lifted via the Hopf fibration . We also show that such submanifolds always satisfy Chen's equality, i.e. , where for every . Then we consider 3-dimensional totally real submanifolds which are linearly full in and which satisfy Chen's equality. We classify such submanifolds as tubes of radius in the direction of the second normal space over an almost complex curve in .

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Additional Information

**Franki Dillen**

Affiliation:
Katholieke Universiteit Leuven, Departement Wiskunde, Celestijnenlaan 200 B, B-3001 Leuven, Belgium

Email:
Franki.Dillen@wis.kuleuven.ac.be

**Luc Vrancken**

Affiliation:
Katholieke Universiteit Leuven, Departement Wiskunde, Celestijnenlaan 200 B, B-3001 Leuven, Belgium

Email:
Luc.Vrancken@wis.kuleuven.ac.be

DOI:
https://doi.org/10.1090/S0002-9947-96-01626-1

Received by editor(s):
April 19, 1995

Additional Notes:
The authors are Senior Research Assistants of the National Fund for Scientific Research (Belgium).

The authors would like to thank J. Bolton and L.M. Woodward for helpful discussions.

Article copyright:
© Copyright 1996
American Mathematical Society