%0 Journal Article %T Tensor-Centric Warfare IV: Kähler Dynamics of Battlefields %A Vladimir Ivancevic %A Darryn Reid %A Peyam Pourbeik %J Intelligent Control and Automation %P 123-146 %@ 2153-0661 %D 2018 %I Scientific Research Publishing %R 10.4236/ica.2018.94010 %X This paper presents the complex dynamics synthesis of the combat dy-namics series called tensor-centric warfare (TCW; for the first three parts of the series, see [1] [2] [3]), which includes tensor generalization of classical Lanchester-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 battle-vectorfield, using dynamics on Kähler manifolds as a rigorous framework for extending the TCW concept. The global Kähler dynamics framework, with its rigorous underpinning called the Kähler-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. %K Tensor-Centric Warfare %K Kä %K hler Geometry %K Complex Battle-Vectorfield %K Lagrangian and Hamiltonian Battlefields %K Kä %K hler-Ricci Flow %K Entropic Computational Wargaming %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=88506