Infinitesimal automorphisms and second variation of the energy for harmonic foliations

DOI10.2748/tmj/1178229154zbMath0488.57009OpenAlexW1980857964MaRDI QIDQ1166164

Franz W. Kamber, Philippe Tondeur

Publication date: 1982

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178229154

zbMATH Keywords

bundle-like metriccurvature properties in the normal bundle of a Riemannian foliationdeformations through harmonic foliationsenergy functional for foliationsHarmonic Riemannian foliationsinfinitesimal metric automorphismsnon-existence of normal Jacobi fieldsnormal Ricci operatorvanishing of Killing vector fields

Mathematics Subject Classification ID

Foliations (differential geometric aspects) (53C12) Variational problems in infinite-dimensional spaces (58E99) Foliations in differential topology; geometric theory (57R30)

Related Items

The Index of Harmonic Foliations on Spheres, Liouville type theorem for transversally harmonic maps, Harmonic foliations on a compact Riemannian manifold of non-negative constant curvature, Transversal infinitesimal automorphisms for harmonic Kähler foliations, Transverse conformal Killing forms on Kähler foliations, Variation formulas for transversally harmonic and biharmonic maps, Liouville type theorem for \((\mathcal{F},\mathcal{F}')_p\)-harmonic maps on foliations, Generalized Obata theorem and its applications on foliations, Transversally holomorphic maps between Kähler foliations, \(L^2\)-transverse conformal Killing forms on complete foliated manifolds, Instability for harmonic foliations on compact homogeneous spaces, Unnamed Item, \(A_{\nu}\)-operator on complete foliated Riemannian manifolds, The non-existence of Killing fields, Riemannian foliations admitting transversal conformal fields. II, TRANSVERSAL INFINITESIMAL AUTOMORPHISMS ON KÄHLER FOLIATIONS

Cites Work

• On the spectral theory of elliptic differential operators. I
• La formule de la variation seconde de l'energie au voisinage d'une application harmonique
• Foliated bundles and characteristic classes
• Foliated manifolds with bundle-like metrics
• The Index of Harmonic Foliations on Spheres
• Curvature structures and conformal transformations
• Harmonic Mappings of Riemannian Manifolds
• Vector fields and Ricci curvature
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