Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2005
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/math/0509267 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We study the indefinite metric $G$ in the contact phase space $(P,θ)$ of a homogeneous thermodynamical system introduced by R. Mrugala. We calculate the curvature tensor, Killing vector fields, second fundamental form of Legendre submanifolds of $P$ - constitutive surfaces of different homogeneous thermodynamical systems. We established an isomorphism of the space $(P,θ,G)$ with the Heisenberg Lie group $H_{n}$ endowed with the right invariant contact structure and the right invariant indefinite metric. The lift $\tG$ of the metric $G$ to the symplectization $\tP$ of contact space $(P,θ)$, its curvature properties, and its Killing vector fields are studied. Finally we introduce the "hyperbolic projectivization" of the space $(\tP,{\tilde θ}, \tG)$ that can be considered as the natural {\bf compactification} of the thermodynamical phase space $(P,θ, G).$