Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 36 (1995), No. 2
M. Belger, V. Milousheva, G. Stanilov:
Jacobi Maps Between Riemannian Manifolds
Abstract
In the present paper we define the notion of Jacobi map between
two Riemannian manifolds as a diffeomorphism, preserving the Jacobi
operator. The main results are: non-trivial Jacobi maps exist only
between locally conformal flat \R manifolds; the Jacobi class of a \R \m
consists of all locally conformal flat \R manifolds, for which the
Jacobi map commutes with the corresponding Ricci operators. Remarks
about the invariance of the eigenvalues and eigenvectors of Jacobi
operators are given.