Flat 3-manifolds with diagonal metrics and applications to warped products
Adara M. Blaga, Dan Radu Latcu
TL;DR
This paper characterizes flat 3-manifolds with diagonal metrics and explores their applications to various warped product manifolds, providing conditions for flatness and nonexistence results.
Contribution
It offers necessary and sufficient conditions for flatness in diagonal metric 3-manifolds and applies these to classify flat warped product-type manifolds.
Findings
Characterization of flat diagonal metric 3-manifolds
Conditions for flat warped, biwarped, and doubly warped products
Nonexistence results for certain warped product manifolds
Abstract
We provide necessary and sufficient conditions for a -dimensional submanifold of 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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Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Computational Geometry and Mesh Generation