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Lower bounds for the eigenvalue of the transversal Dirac operator on a Kähler foliation

✍ Scribed by Seoung Dal Jung; Tae Ho Kang

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
140 KB
Volume
45
Category
Article
ISSN
0393-0440

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✦ Synopsis

On a foliated Riemannian manifold with a Kähler spin foliation, we give a lower bound for the square of the eigenvalues of the transversal Dirac operator. We prove, in the limiting case, that the foliation is a minimal, transversally Einsteinian of odd complex dimension with nonnegative constant transversal scalar curvature.

📜 SIMILAR VOLUMES

Upper bounds for the first eigenvalue of
Upper bounds for the first eigenvalue of the Dirac operator on surfaces
✍ Ilka Agricola; Thomas Friedrich 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 734 KB

In this paper we will prove new extrinsic upper bounds for the eigenvalues of the Dirac operator on an isometrically immersed surface M 2 ~ ~3 as well as intrinsic bounds for two-dimensional compact manifolds of genus zero and genus one. Moreover, we compare the different estimates of the eigenvalue