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Non‐Existence of Stable Harmonic Maps from Sufficiently Pinched Simply Connected Riemannian Manifolds
Author(s) -
Yanglian Pan
Publication year - 1989
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-39.3.568
Subject(s) - riemannian manifold , mathematics , simply connected space , constant (computer programming) , harmonic map , manifold (fluid mechanics) , dimension (graph theory) , exponential map (riemannian geometry) , pure mathematics , harmonic , mathematical analysis , riemannian geometry , pseudo riemannian manifold , sectional curvature , ricci curvature , geometry , physics , scalar curvature , curvature , computer science , mechanical engineering , quantum mechanics , engineering , programming language
It is proved that for n ⩾ 3 there exists a constant δ( n ) with ¼ ⩽ δ( n ) < 1 such that if M is a simply connected Riemannian manifold of dimension n with δ( n )‐pinched curvatures then for every Riemannian manifold N every stable harmonic map φ: M → N is constant. Together with Howard's result, this shows that a simply connected sufficiently pinched Riemannian manifold is weakly E ‐unstable.