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Dedicated to Professor Shigeru Ishihara on his seventieth birthday
The authors thanks the referee for his kind suggestions
This research was partially supported by TGRC-KOSEF and by the Basic Science Research Institute Program, Ministry of Education, 1996, Project No. BSRI-96-1404.
Recently the authors were informed that this result was extended to general compact manifolds of dimension grater than 2 by Colbois and Dodziuk ([5]), namely
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Kang, T.H., Pak, H.K. & Pak, J.S. Laplacian on a totally geodesic foliation. J Geom 60, 74–79 (1997). https://doi.org/10.1007/BF01252218
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DOI: https://doi.org/10.1007/BF01252218