The Geometry of Maximal Flat Submanifolds of Symmetric Spaces
Bart Michels (LAGA)
TL;DR
This paper explores the geometric properties of maximal flat submanifolds in symmetric spaces of non-compact type, extending classical hyperbolic geodesic results to a broader geometric context.
Contribution
It generalizes known properties of hyperbolic geodesics to maximal flat submanifolds in symmetric spaces, motivated by spectral asymptotics in trace formulas.
Findings
Extended geometric properties from hyperbolic geodesics to flat submanifolds
Provided new insights into spectral asymptotics for orbital integrals
Connected geometric analysis with representation theory and trace formulas
Abstract
Motivated by spectral asymptotics for orbital integrals in a relative trace formula, we generalize a number of geometric properties of geodesics in the hyperbolic plane, to maximal flat submanifolds of symmetric spaces of non-compact type.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology