Artikel
Lizenziert
Nicht lizenziert
Erfordert eine Authentifizierung
Some theorems of harmonic maps for Finsler manifolds
-
J. T. Li
Veröffentlicht/Copyright:
8. Juli 2014
Abstract
We study some properties of harmonic maps for Finsler manifolds and present two theorems: (1) every non-degenerate harmonic map ϕ from a compact Riemannian manifold with nonnegative Ricci curvature to a Berwald manifold with non-positive flag curvature is totally geodesic; this improves a result of He and Shen [3]. (2) Let M be a compact Riemannian manifold with non-negative Ricci curvature and let M‾ be a complete Finsler manifold with non-positive flag curvature. Then every non-degenerate smooth map ϕ : M → M with trb▽̃dϕ = 0 is totally geodesic; this generalizes a result of Eells and Sampson [2] from the Riemannian case to the Finsler case.
Published Online: 2014-7-8
Published in Print: 2014-7-1
© 2014 by Walter de Gruyter Berlin/Boston
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Artikel in diesem Heft
- Masthead
- On axiomatic definitions of non-discrete affine buildings
- On Clifford analysis for holomorphic mappings
- Universal points of convex bodies and bisectors in Minkowski spaces
- The equal tangents property
- Some theorems of harmonic maps for Finsler manifolds
- The regular Grünbaum polyhedron of genus 5
- On the existence of nilsolitons on 2-step nilpotent Lie groups
- Rotational linear Weingarten hypersurfaces in the Euclidean sphere Sn+1
- Spacelike hypersurfaces in anti-de Sitter space
- The group of strong symplectic homeomorphisms in the L∞-metric
- The total Betti number of the intersection of three real quadrics
- On the algebraic models of symmetric smooth manifolds
- Non-existence of tight neighborly triangulated manifolds with β1 = 2
Artikel in diesem Heft
- Masthead
- On axiomatic definitions of non-discrete affine buildings
- On Clifford analysis for holomorphic mappings
- Universal points of convex bodies and bisectors in Minkowski spaces
- The equal tangents property
- Some theorems of harmonic maps for Finsler manifolds
- The regular Grünbaum polyhedron of genus 5
- On the existence of nilsolitons on 2-step nilpotent Lie groups
- Rotational linear Weingarten hypersurfaces in the Euclidean sphere Sn+1
- Spacelike hypersurfaces in anti-de Sitter space
- The group of strong symplectic homeomorphisms in the L∞-metric
- The total Betti number of the intersection of three real quadrics
- On the algebraic models of symmetric smooth manifolds
- Non-existence of tight neighborly triangulated manifolds with β1 = 2
