Adapted complex and involutive structures
L\'aszl\'o Lempert
TL;DR
This paper introduces and analyzes complex and involutive structures on spaces of geodesics and harmonic maps, focusing on their existence, uniqueness, and symmetry compatibility.
Contribution
It defines generalized complex structures on these spaces and establishes conditions for their existence and uniqueness, advancing geometric analysis.
Findings
Existence of complex structures on spaces of geodesics and harmonic maps.
Uniqueness results for these structures under symmetry conditions.
Compatibility of structures with space symmetries.
Abstract
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Nonlinear Waves and Solitons