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The rigidity theorem for harmonic maps from Berwald manifolds. (English) Zbl 1327.53099

Summary: In this paper, we can prove that any non-degenerate strongly harmonic map \(\phi\) from a compact Berwald manifold with nonnegative general Ricci curvature to a Landsberg manifold with non-positive flag curvature must be totally geodesic, which generalizes the result of J. Eells jun. and J. H. Sampson [Am. J. Math. 86, 109–160 (1964; Zbl 0122.40102)].

MSC:

53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
53C43 Differential geometric aspects of harmonic maps

Citations:

Zbl 0122.40102
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References:

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