DRM: Directional Relational Manifolds
Authors/Creators
Description
We introduce Directional Relational Manifolds (DRM), a class of geometrical structures in
which dimensionality is not fixed but emerges dynamically from relational directional fields. Unlike
classical manifolds based on orthogonal tangent spaces, DRMs define dimensions as active direc-
tions whose structure may vary locally and globally. We develop the formal foundations of DRM,
define its metric, connection, curvature, and dynamics, and show that stable DRMs naturally
converge to toroidal topology. DRM extends information geometry [Amari and Nagaoka(2000)]
from the fixed-dimension setting to variable-dimension structures, reducing to the Fisher–Rao
framework as a special case. This framework provides a unified mathematical language for
adaptive physical, cognitive, and informational systems.
Files
DRM__Directional_Relational_Manifolds_V1_1.pdf
Files
(280.4 kB)
| Name | Size | Download all |
|---|---|---|
|
md5:e8ad69f602ce23a702eebaf6d1f78269
|
280.4 kB | Preview Download |
Additional details
References
- S. Amari and H. Nagaoka. Methods of Information Geometry. American Mathematical Society, 2000.
- N. N. Chentsov. Statistical Decision Rules and Optimal Inference. American Mathematical Society, 1982.
- A. Katok and B. Hasselblatt. Introduction to the Modern Theory of Dynamical Systems. Cambridge University Press, 1995.
- F. Nielsen. An elementary introduction to information geometry. 22(10):1100, 2020. arXiv:1808.08271.