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.
Frosini P., Landi C. (2003). Intrinsic harmonicity of morse functions. MATHEMATIKA, 50(1-2), 167-170 [10.1112/S002557930001487X].
Intrinsic harmonicity of morse functions
Frosini P.;Landi C.
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.File in questo prodotto:
Eventuali allegati, non sono esposti
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.