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I’m a first-year graduate math student on my way to earn my master's. I like geometry and topology and our faculty has two geometers and hence I have two options for the thesis. First is walker manifolds and semi-Riemannian geometry and second, Finsler geometry. At present I don't have any knowledge or intuition neither on these topics nor on the levels of their difficulty compared with each other. So I would appreciate any explanations/directions as to whether the two subjects (or either of them) are currently active areas of research in the math community and their current status in science.

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