Riemannov tenzor zakrivljenosti

Abstract

U ovom radu prvo navodimo neka svojstva regularnih ploha u $\mathbb{R}^3$, kao što je pojam Riemannovog tenzora definiran na tim plohama, i navodimo dokaz Gaussovog Veličanstvenog teorema. Nakon toga navodimo osnove diferencijalnih mnogostrukosti uključujući i pojam Riemannove metrike. Zatim obradujemo pojam Riemannovih mnogostrukosti i proučavamo neka njihova svojstva.In this thesis we first recall some properties of the regular surfaces in $\mathbb{R}^3$, like the notion of the Riemann tensor of this surfaces and present a proof of the Gauss’s Theorema Egregium. Afterwards we present basics of Differential manifolds including a concept of the Riemannian metric on. Then we elaborate the notion of a Riemannian manifolds and study some of its properties