Tohoku Mathematical Journal
2009
December
SECOND SERIES VOL. 61, NO. 4

Tohoku Math. J.
61 (2009), 441-453

Title NEW ESTIMATES FOR EIGENVALUES OF THE BASIC DIRAC OPERATOR

Author Seoung Dal Jung, Soon Chan Kim and Jeong Hyeong Park

(Received December 12, 2008, revised April 16, 2009)
Abstract. On a transverse spin foliation, we give a new lower bound for the square of the eigenvalues of the basic Dirac operator by the smallest eigenvalue of the basic Yamabe operator. Moreover, the limiting foliation is transversally Einsteinian.

2000 Mathematics Subject Classification. Primary 53C43; Secondary 58E20.
Key words and phrases. The basic Dirac operator, transverse spin foliation, transversally Einsteinian.

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