[Untitled]
In: Letters in Mathematical Physics, Jg. 54 (2000), S. 193-201
Online
unknown
Zugriff:
Let two Riemannian metrics g and g on one manifold Mn have the same geodesics (considered as unparameterized curves). Then we can construct invariantly n commuting differential operators of second order. The Laplacian Δg of the metric g is one of these operators. For any x ∈ Mn, consider the linear transformation G of TxMn given by the tensor gIαgαj. If all eigenvalues of G are different at one point of the manifold then they are different at almost every point; the operators are linearly independent and their symbols are functionally independent. If all eigenvalues of G are different at each point of a closed manifold then it can be covered by the n-torus and we can globally separate the variables in the equation Δgf = μf on this torus.
Titel: |
[Untitled]
|
---|---|
Autor/in / Beteiligte Person: | Matveev, Vladimir S. |
Link: | |
Zeitschrift: | Letters in Mathematical Physics, Jg. 54 (2000), S. 193-201 |
Veröffentlichung: | Springer Science and Business Media LLC, 2000 |
Medientyp: | unknown |
ISSN: | 0377-9017 (print) |
DOI: | 10.1023/a:1010851911925 |
Schlagwort: |
|
Sonstiges: |
|