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August 30th, 2018
09:25 am
https://lj.rossia.org/users/mathematiker/4177.html?thread=51281#t51281
кстати, зачем существует курс ``differential geoemtry of curves and surfaces''
вместе с курсом ``differential geoemtry'' c содержанием вроде ``lie groups and
lie algebras, action of the lie group on varieties, vector bundles and fibered
manifolds, principal and associated bundles, connections on principal bundles,
parallel transports, linear connections on vector bundles, riemannian metric and
its levi-civita connection, ...''?
можно ли взять второй курс, не взяв предварительно первого? в смысле, нет ли там
чего-нибудь важного, что упускать никак нельзя. речь в моём случае конкретно про
этот курс: https://is.muni.cz/predmet/sci/M7110?lang=en
Prerequisites
M5130 Global Analysis Before enrolling the course the students should pass
"Differential Geometry of Curves and Surfaces" and "Global Analysis".
и про первый:
Syllabus
Parametric expressions and equations of curves and surfaces. Contact of two
curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature
and torsion of spacial curves. Envelops. The first and the second fundamental
form of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
вот, например, что пишут об этом на math.stackexchange.com:
You won't miss much by dropping curves and surfaces: every important article
I studied, browsed or heard about published in the last 60 years in differential
geometry by such luminaries as Thom, Milnor, Atiyah, Hirzebruch,
Perelman,...contains little or no reference to curves and surfaces. On the
other hand if you spend your time on Codazzi equations, Frenet-Serret frames and
umbilic points you might have no time left for principal bundles,
Stiefel-Whitney or Chern classes, cobordism,etc. and that means you will have
little chance of understanding anything in modern differential geometry. Of
course it would be great to combine the mastery of both the exquisitely detailed
classical results in one or two dimensions and the general powerful modern
techniques of differential geometry/topology, but if you want to arrive at the
frontier of research in a reasonable time you will have to favour the latter
over the former.
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