Minimal Lagrangian submanifolds with constant sectional curvature in indefinite complex space forms

Author:
Luc Vrancken

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1459-1466

MSC (2000):
Primary 53B25, 53B30

DOI:
https://doi.org/10.1090/S0002-9939-01-06213-X

Published electronically:
October 17, 2001

MathSciNet review:
1879970

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Abstract: We study minimal Lagrangian immersions from an indefinite real space form into an indefinite complex space form . Provided that , we show that has to be flat and we obtain an explicit description of the immersion. In the case when the metric is positive definite or Lorentzian, this result was respectively obtained by Ejiri (1982) and by Kriele and the author (1999). In the case that , this theorem is no longer true; see for instance the examples discovered by Chen and the author (accepted for publication in the Tôhoku Mathematical Journal).

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Additional Information

**Luc Vrancken**

Affiliation:
Mathematisch Instituut, Universiteit Utrecht, Budapestlaan 6, 3584CD Utrecht, The Netherlands

Email:
vrancken@math.uu.nl

DOI:
https://doi.org/10.1090/S0002-9939-01-06213-X

Keywords:
Lagrangian,
constant sectional curvature,
indefinite complex space forms

Received by editor(s):
October 7, 1999

Received by editor(s) in revised form:
November 10, 2000

Published electronically:
October 17, 2001

Additional Notes:
This work was partially supported by a research fellowship of the Alexander von Humboldt Stiftung (Germany)

Communicated by:
Christopher Croke

Article copyright:
© Copyright 2001
American Mathematical Society