Flat 3-manifolds with diagonal metrics and applications to warped products
Abstract
We provide necessary and sufficient conditions for a 3-dimensional submanifold of R3 endowed with a diagonal metric to be flat. As applications, we characterize the flat manifolds of warped product-type, more precisely, the warped, biwarped, sequential warped, and doubly warped product manifolds, and we state the corresponding nonexistence results.
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