A characterization of minimal Legendrian submanifolds in S^(2n+1)

Hông Vân Lê and Guofang Wang

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Submission date: 29. Feb. 2000
Pages: 9
published in: Compositio mathematica, 129 (2001) 1, p. 87-93 
DOI number (of the published article): 10.1023/A:1013190332022
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Abstract:
Let be a minimal submanifold in . In this note, we show that L is Legendrian if and only if for any the restriction to L of satisfies D f=2(n+1)f. In this case, 2(n+1) is an eigenvalue of the Laplacian with multiplicity at least . Moreover if the multiplicity equals to , then is totally geodesic.