Tensor-Centric Warfare Ⅳ: Kaehler Dynamics of Battlefields

摘要

This paper presents the complex dynamics synthesis of the combat dynamics series called tensor-centric warfare (TCW; for the first three parts of the series, see [1] [2] [3]), which includes tensor generalization of classical Lan-chester-type combat equations, entropic Lie-dragging and commutators for modeling warfare uncertainty and symmetry, and various delta-strikes and missiles (both deterministic and random). The present paper gives a unique synthesis of the Red vs. Blue vectorfields into a single complex bat-tle-vectorfield, using dynamics on Kaehler manifolds as a rigorous framework for extending the TCW concept. The global Kaehler dynamics framework, with its rigorous underpinning called the Kaehler-Ricci flow, provides not only a new insight into the "geometry of warfare", but also into the "physics of warfare", in terms of Lagrangian and Hamiltonian structures of the battlefields. It also provides a convenient and efficient computational framework for entropic wargaming.