Pfaffian

Dasar-Dasar Optika Geometri

“…[33] Gauss-Bonnet formula expresses the global invariant, χ(M ), as the integral of a local invariant, which is perhaps the most desirable relationship between local and global properties [389]. For even-dimensional oriented compact Riemannian manifold, M 2n , the Gauss-Bonnet-Chern theorem is a special case of the Atiyah-Singer index theorem [390].…”

“…In the case of the non-linear optics, the pfaffian of Ω (12. The Gauss-Bonnet-Chern theorem 10 says that [374,390] (…”

“…For even-dimensional oriented compact Riemannian manifold, M 2n , the Gauss-Bonnet-Chern theorem is a special case of the Atiyah-Singer index theorem [390]. In the case of the linear optics, the Gauss-Bonnet-Chern theorem (12.26) becomes…”

“…Shortly, the pfaffian of Ω (14. Using the pfaffian of Ω, the Gauss-Bonnet-Chern theorem [389,390,391] says that [374,390] (−1) q 1 2 2q π q q! M 2q pf Ω = χ(M 2q ) (14.22) where χ(M 2q ) is the Euler-Poincare characteristic [392,393] (a topological invariant [374], a global invariant [389]) of the even dimensional oriented compact Riemannian manifold, M 2q .…”

Matematika Fisika Teoretika

“…Teorema Gauss-Bonnet-Chern 3 menyatakan bahwa [7,13] ( 3 Formula Gauss-Bonnet menyatakan ketakubahan global, χ(M ), sebagai integral ketakubahan lokal, barangkali merupakan hubungan yang paling diinginkan antara sifat lokal dan sifat global [12].…”