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We found one dictionary that defines the word geodesicity:

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  1. geodesicity: Wiktionary

Definitions from Wiktionary (geodesicity)

noun:  (mathematics) The property of a smooth curve being a geodesic or of a vector field to be geodesic in the context of differential geometry.
noun:  (mathematics) The characterisation of a differentiable manifold in terms of its geodesics, such as the quality of a submanifold being totally geodesic.

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