Finslerova geometriya odne z uzagalnen rimanovoyi geometriyi U finslerovij geometriyi rozglyadayutsya mnogovidi z finslerovim metrichnim tenzorom tobto viborom gladkoyi normi na kozhnomu dotichnomu prostori yaka gladko zminyuyetsya vid tochki do tochki Osnovni ponyattya red Nehaj M n displaystyle M n nbsp n displaystyle n nbsp vimirnij zv yazanij C displaystyle C infty nbsp mnogovid Poznachimo cherez T M n displaystyle TM n nbsp dotichne rozsharuvannya M n displaystyle M n nbsp Todi finslerovoyu metrikoyu na M n displaystyle M n nbsp nazivayetsya funkciya F T M n 0 displaystyle F colon TM n rightarrow 0 infty nbsp sho zadovilnyaye vlastivostyam F C T M n 0 displaystyle F in C infty TM n setminus 0 nbsp F displaystyle F nbsp dodatno odnorodna pershoyi stepeni tobto dlya bud yakoyi pari x y T M n displaystyle x y in TM n nbsp i chisla l gt 0 displaystyle lambda gt 0 nbsp F x l y l F x y displaystyle F x lambda y lambda F x y nbsp Dlya bud yakoyi pari x y T M n displaystyle x y in TM n nbsp bilinijna forma g y T x M n T x M n R displaystyle mathbf g y colon T x M n times T x M n rightarrow mathbb R nbsp g y u v 1 2 2 t s F 2 x y s u t v s t 0 displaystyle mathbf g y u v frac 1 2 frac partial 2 partial t partial s lbrack F 2 x y su tv rbrack s t 0 nbsp dodatno viznachena Dzherela red H Rund The Differential Geometry of Finsler Spaces Springer Verlag 1959 ASIN B0006AWABG Otrimano z https uk wikipedia org w index php title Finslerova geometriya amp oldid 23171502
