Intrinsic harmonicily of Morse functions | Zendy

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Intrinsic harmonicily of Morse functions

Author(s) -

Frosini Patrizio,

Landi Claudia

Publication year - 2003

Publication title -

mathematika

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.955

H-Index - 29

eISSN - 2041-7942

pISSN - 0025-5793

DOI - 10.1112/s002557930001487x

Subject(s) - mathematics , morse code , morse theory , metric (unit) , riemannian manifold , manifold (fluid mechanics) , pure mathematics , circle valued morse theory , closed manifold , set (abstract data type) , harmonic , harmonic function , mathematical analysis , combinatorics , invariant manifold , mechanical engineering , operations management , physics , quantum mechanics , computer science , electrical engineering , economics , programming language , engineering

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 of f 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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