Diferenciální invarianty metrického tenzoru
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Vysoká škola báňská – Technická univerzita Ostrava
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Abstract
This thesis discusses, on an introductory level, the theory of differential invariants and their construction
using the “orbit reduction method“, which consists of the decomposition of differential invariants by means
of suitable factorization of the domain. In our case, it is a space of 2.-nd order metric tensors,
on which acts a differential group (generalizing general linear group). From the point of view of
this theory, we discuss the famous Hilbert Lagrangian in general relativity theory, and we show that it
results in scalar invariance of the metric tensor
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differential invariant, differential group, metric tensor, fibre bundle, Hilbert Lagrangian