Exploring Holonomic Basis in Cartesian Coordinates • Physics Forums

mairzydoats · 2021-07-24T16:09:25+00:00

Are cartesian coordinates the only coordinates with a holonomic basis that's orthonormal everywhere?

Thread 'Injective immersion and embedding'

Hello! There is a simple line in the textbook. If ##S## is a manifold, an injectively immersed submanifold ##M## of ##S## is embedded if and only if ##M## is locally closed in ##S##. Recall the definition. M is locally closed if for each point ##x\in M## there open ##U\subset S## such that ##M\cap U## is closed in ##U##. Embedding to injective immesion is simple. The opposite direction is hard. Suppose I have ##N## as source manifold and ##f:N\rightarrow S## is the injective...

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B Exploring Holonomic Basis in Cartesian Coordinates

Thread 'Injective immersion and embedding'

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