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A characterization of harmonic sections and a Liouville theorem

Simão Stelmastchuk (2012)

Archivum Mathematicum

Let $P (M, G)$ be a principal fiber bundle and $E (M, N, G, P)$ an associated fiber bundle. Our interest is to study the harmonic sections of the projection $π_{E}$ of $E$ into $M$ . Our first purpose is give a characterization of harmonic sections of $M$ into $E$ regarding its equivariant lift. The second purpose is to show a version of a Liouville theorem for harmonic sections of $π_{E}$ .

A characterization of the Riemann extension in terms of harmonicity

Cornelia-Livia Bejan, Şemsi Eken (2017)

Czechoslovak Mathematical Journal

If $(M, \nabla)$ is a manifold with a symmetric linear connection, then $T^{*} M$ can be endowed with the natural Riemann extension $\bar{g}$ (O. Kowalski and M. Sekizawa (2011), M. Sekizawa (1987)). Here we continue to study the harmonicity with respect to $\bar{g}$ initiated by C. L. Bejan and O. Kowalski (2015). More precisely, we first construct a canonical almost para-complex structure $𝒫$ on $(T^{*} M, \bar{g})$ and prove that $𝒫$ is harmonic (in the sense of E. García-Río, L. Vanhecke and M. E. Vázquez-Abal (1997)) if and only if $\bar{g}$ reduces to the...

Currently displaying 1 – 20 of 313

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Displaying 1 – 20 of 313

A characterization of harmonic sections and a Liouville theorem

A characterization of the Riemann extension in terms of harmonicity

A classification and some constructions of $p$ -harmonic morphisms.

A compactness theorem of n-harmonic maps

A finiteness theorem of harmonic maps form compact Lie groups to OHS(H).

A generalization of the Schwarz-Ahlfors lemma fo the theory of harmonic maps.

A Geometric Characterization of Harmonic Diffeomorphisms Between Surfaces.

A geometric construction of (para)-pluriharmonic maps into $G L (2 r) / S P (2 r)$ .

A Liouville theorem for $F$ -harmonic maps with finite $F$ -energy.

A Liouville type theorem for $p$ -harmonic functions on minimal submanifolds in $ℝ^{n + m}$

A Maximum Principle for Harmonic Mappings Which Solve A Dirichlet Problem.

A minimising property of the radial projection.

A mixed boundary value problem for energy minimizing harmonic maps.

A monotonicity formula for Yang-Mills Fields.

A Non-Existence Theorem for Pluriharmonic Maps of Finite Energy.

A note on Bochner type theorems for complete manifolds.

A note on harmonic maps between surfaces

A priori estimates for harmonic mappings.

A regularity theorem for harmonic mappings.

A Remark on H1 Mappings.

Currently displaying 1 – 20 of 313