A new type of topological electron transition in metals with changing Fermi energy

A new type of topological electron transition occurred with a jump-like change in the differential-geometrical characteristics of the Fermi surface (without any modification of its topology) at a certine critical energy εd is predicted. This type of transition differs from the known ones, which are associated with a modification of the Fermi surface topology, in that the constant-energy surface, ε(p)=εd , does not contain particular points at which the electron velocity becomes zero. It is shown that common to these two types of electron topological transitions responsible for by the jump-like changes in the Fermi surface topology and its differential-geometrical characteristics without any modification of topology, is a qualitative change of the spherical image of Fermi surface agreed upon a jump-like change of the number of pre-images under the spherical mapping