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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
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 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.