Lichnerowicz and Obata theorems for foliations.

DOI10.2140/pjm.2002.206.339zbMath1060.53037OpenAlexW1971432627WikidataQ125096776 ScholiaQ125096776MaRDI QIDQ1858329

Ken V. Richardson, Jeffrey M. Lee

Publication date: 13 February 2003

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.2002.206.339

zbMATH Keywords

Ricci curvatureRiemannian foliationmean curvaturebasic Laplacian

Mathematics Subject Classification ID

Foliations (differential geometric aspects) (53C12) Partial differential equations on manifolds; differential operators (58J99) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (15)

Eigenvalue estimate for the basic Laplacian on manifolds with foliated boundary ⋮ The wave trace of the basic Laplacian of a Riemannian foliation near a non-zero period ⋮ The singularities of the wave trace of the basic Laplacian of a Riemannian foliation ⋮ Modified differentials and basic cohomology for Riemannian foliations ⋮ Eigenvalue estimates for 3-Sasaki structures ⋮ Generalized Obata theorem and its applications on foliations ⋮ Riemannian foliations admitting transversal conformal fields ⋮ The \(\mathrm{G}_2\) geometry of 3-Sasaki structures ⋮ Transverse conformal Killing forms and a Gallot-Meyer theorem for foliations ⋮ A lower bound on the spectrum of the Sublaplacian ⋮ The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds ⋮ Lower bounds for the eigenvalues of the basic Dirac operator on a Riemannian foliation ⋮ Wave Invariants of the Spectrum of theG-Invariant Laplacian and the Basic Spectrum of a Riemannian Foliation ⋮ Unnamed Item ⋮ Riemannian foliations admitting transversal conformal fields. II

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