First eigenvalue of the Laplacean and torsion of parallelizable Riemannian manifolds
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- by Patrick Ghanaat PDF
- Proc. Amer. Math. Soc. 107 (1989), 807-810 Request permission
Abstract:
Lower and upper bounds for the smallest positive eigenvalue of the Laplacean on a parallelizable Riemannian manifold are combined to obtain an explicit lower bound for the torsion of global orthonormal frame fields in terms of the diameter of the metric.References
- Patrick Ghanaat, Almost Lie groups of type $\textbf {R}^n$, J. Reine Angew. Math. 401 (1989), 60–81. MR 1018053, DOI 10.1515/crll.1989.401.60
- M. Gromov, Almost flat manifolds, J. Differential Geometry 13 (1978), no. 2, 231–241. MR 540942
- L. E. Payne and H. F. Weinberger, An optimal Poincaré inequality for convex domains, Arch. Rational Mech. Anal. 5 (1960), 286–292 (1960). MR 117419, DOI 10.1007/BF00252910
- Ernst A. Ruh, Almost Lie groups, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp. 561–564. MR 934256
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 107 (1989), 807-810
- MSC: Primary 58G25; Secondary 53C20, 57R25
- DOI: https://doi.org/10.1090/S0002-9939-1989-0990423-X
- MathSciNet review: 990423