Consider a real valued Morse function f on a C-2 closed connected n-dimensional manifold M. It is proved that a suitable Riemannian metric exists on M, such that f is harmonic outside the set of critical points off of index 0 and n. The proof is based on a result of Calabi [1], providing a criterion for a closed one-form on a closed connected manifold to be harmonic with respect to some Riemannian metric.
Intrinsic harmonicity of Morse functions / P., Frosini; Landi, Claudia. - In: MATHEMATIKA. - ISSN 0025-5793. - STAMPA. - 50:(2003), pp. 167-170. [10.1112/S002557930001487X]
Intrinsic harmonicity of Morse functions
LANDI, Claudia
2003
Abstract
Consider a real valued Morse function f on a C-2 closed connected n-dimensional manifold M. It is proved that a suitable Riemannian metric exists on M, such that f is harmonic outside the set of critical points off of index 0 and n. The proof is based on a result of Calabi [1], providing a criterion for a closed one-form on a closed connected manifold to be harmonic with respect to some Riemannian metric.
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