Finsler Surfaces

Theory of Finsler Submanifolds via Berwald Connection

“…Note that n i α , n i αβ and n i αβγ are the local components of some mixed Finsler tensor fields on F m with respect to the vector bundle V T M |T M (cf. Bejancu [5], p. 34). Now, we can state the main result of this section.…”

“…where ∇ is the linear connection from the Berwald connection BF C of F m+p given by (2.22). Therefore BF C = (HT M, ∇) is a vectorial Finsler connection on F m with respect to the vector bundle V T M |T M (see Bejancu [5], p. 26). By (2.40) and (2.22) we deduce that ∇ is locally given by (2.41)…”

“…Finally, the structure equations obtained so far have cumbersome forms which are almost impossible to be used in a study of the geometry of a concrete Finsler submanifold. Several people have made some fundamental contributions to the subject: Akbar Zadeh [1], Barthel [3], Bejancu [4], [5], Bejancu-Farran [6], [7], Comic [8], Haimovici [9], Matsumoto [10], [11], Miron [13], Rund [14], Shen [15], Varga [17], Wegener [18].…”

“…In the first section we arrange some basic formulae from Finsler geometry and recall the main properties of vectorial Finsler connections (cf. Bejancu [5]). Next, in Section 2 we relate the Berwald connections on both F m and F m+p (cf.…”

Finsler geometry of nonlinear elastic solids with internal structure

“…See also the overview article by Eringen [4]. Extensions to pseudo-and generalized Finsler geometries are described in the monograph of Bejancu [5] and research cited therein [6][7][8], as well as several more recent works [9,10].…”