3 papers
math.GM2025
Exceptional Symmetry as a Source of Algebraic Cycles: Non-Constructive Methods for the Hodge Conjecture for a Special Class of Calabi-Yau 5-Folds
Dongzhe Zheng
Classical variational Hodge structure theory characterizes the algebraicity of Hodge classes by studying the transversality of period mappings under geometric deformations. However…
math.GM2025
Constrained Hamiltonian Systems on Observation-Induced Fiber Bundles: Theory of Symmetry and Integrability
Dongzhe Zheng
Classical constrained Hamiltonian theory assumes complete observability of system states, but in reality only partial state information is often available. This paper establishes a…
math.GM2025
Dynamical Geometry of Principal Bundle Constrained Systems: Compatible Pairs, Contact Degeneration, and Adapted Metrics
Dongzhe Zheng
We study invariant codimension-one constraints on principal bundles through compatible pairs: a constraint distribution and a nonzero coadjoint field parallel for a principal conne…