About: Lichnerowicz conjecture

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In mathematics, the Lichnerowicz conjecture is a generalization of a conjecture introduced by Lichnerowicz. Lichnerowicz's original conjecture was that locally harmonic 4-manifolds are locally symmetric, and was proved by . The Lichnerowicz conjecture usually refers to the generalization that locally harmonic manifolds are flat or rank-1 locally symmetric. It has been proven true for compact manifolds with fundamental groups that are finite groups but counterexamples exist in seven or more dimensions in the non-compact case

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  • In mathematics, the Lichnerowicz conjecture is a generalization of a conjecture introduced by Lichnerowicz. Lichnerowicz's original conjecture was that locally harmonic 4-manifolds are locally symmetric, and was proved by . The Lichnerowicz conjecture usually refers to the generalization that locally harmonic manifolds are flat or rank-1 locally symmetric. It has been proven true for compact manifolds with fundamental groups that are finite groups but counterexamples exist in seven or more dimensions in the non-compact case (en)
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  • In mathematics, the Lichnerowicz conjecture is a generalization of a conjecture introduced by Lichnerowicz. Lichnerowicz's original conjecture was that locally harmonic 4-manifolds are locally symmetric, and was proved by . The Lichnerowicz conjecture usually refers to the generalization that locally harmonic manifolds are flat or rank-1 locally symmetric. It has been proven true for compact manifolds with fundamental groups that are finite groups but counterexamples exist in seven or more dimensions in the non-compact case (en)
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  • Lichnerowicz conjecture (en)
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