Preprint 9/2000

A characterization of minimal Legendrian submanifolds in S2n+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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Let tex2html_wrap_inline12 be a minimal submanifold in tex2html_wrap_inline14. In this note, we show that L is Legendrian if and only if for any tex2html_wrap_inline18 the restriction to L of tex2html_wrap_inline22 satisfies D f=2(n+1)f. In this case, 2(n+1) is an eigenvalue of the Laplacian with multiplicity at least tex2html_wrap_inline28. Moreover if the multiplicity equals to tex2html_wrap_inline28, then tex2html_wrap_inline32 is totally geodesic.

24.11.2021, 02:11