Lagrangian Mechanics on Quaternion Kaehler Manifolds

Constrained Paracomplex Mechanical Systems

In this study, it is introduced paracomplex analogue of Lagrangians and Hamiltonians with constraints in the framework of para-Kaehlerian manifolds. The geometrical and mechanical results on the constrained mechanical system have also been discussed.

Balanced metrics and noncommutative Kaehler geometry

In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions on a Kahler manifold M. In this setup one interprets M as the phase space itself, equipped with the Poisson brackets inherited from the Kahler 2-form. We compare the geometric quantization framework with several deformation quantization approaches. We find that the balanced metrics appear naturally as a result of setting the vacuum energy to be the constant function on the moduli space of semiclassical vacua. In the classical limit these metrics become Kahler-Einstein (when M a…

几何热力学的宏观Kaehler度量与事件流形上的微观度量：CV流形上的精确配分函数。扩展Souriau温度和自发磁化

The macroscopic Kaehler metric of Geometric Thermodynamics versus the microscopic one on the Event Manifold: Exact Partition Functions on CV manifolds. Extended Souriau temperatures and spontaneous magnetizations

本文阐明了几何热力学与基于Fisher矩阵的信息几何之间的关系，首次在热力学变量的宏观接触流形上引入Kähler度量，并通过CV流形上的精确配分函数积分和Killing矩映射的非线性Casimir函数，推广了Souriau热力学，类比于铁磁自发磁化。