On the Geometry of Complex Grassmann Manifold, Its Noncompact Dual and Coherent States
Stefan Berceanu
TL;DR
This paper surveys the differential geometry of the complex Grassmann manifold, focusing on conjugate loci, distances, and their relation to coherent states, using Jordan's stationary angles for calculations.
Contribution
It provides new formulas for distances and conjugate loci on the complex Grassmann manifold, enhancing geometric understanding related to coherent states.
Findings
Calculated tangent conjugate locus and conjugate locus using Jordan's stationary angles.
Derived formulas for distances on the complex Grassmann manifold.
Connected geometric properties to the theory of coherent states.
Abstract
Different topics on the differential geometry of the complex Grassmann manifold are surveyed in relation to the coherent states. A calculation of the tangent conjugate locus and conjugate locus in the complex Grassmann manifold is presented. The proofs use the Jordan's stationary angles. Also various formulas for the distance on the complex Grassmann manifold are furnished.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds