Natural Poisson and Jacobi structures on the tangent bundle of a pseudo-Riemannian manifold

JANYŠKA, Josef. Natural Poisson and Jacobi structures on the tangent bundle of a pseudo-Riemannian manifold. In Global Differential Geometry: The Mathematical Legacy of Alfred Gray. 1st ed. USA: American Mathematical Society, 2001, p. 343-347. Contemporary Mathematics 288. ISBN 0-8218-2750-2.

Basic information

• Original name: Natural Poisson and Jacobi structures on the tangent bundle of a pseudo-Riemannian manifold
• Authors: JANYŠKA, Josef.
• Edition: 1. vyd. USA, Global Differential Geometry: The Mathematical Legacy of Alfred Gray, p. 343-347, Contemporary Mathematics 288, 2001.
• Publisher: American Mathematical Society

Other information

• Original language: English
• Type of outcome: Proceedings paper
• Field of Study: 10101 Pure mathematics
• Country of publisher: United States of America
• Confidentiality degree: is not subject to a state or trade secret
• RIV identification code: RIV/00216224:14310/01:00005232
• Organization unit: Faculty of Science
• ISBN: 0-8218-2750-2
• Keywords in English: Poisson structure; Jacobi structure; pseudo-Riemannian manifold
• Tags: Jacobi structure, Poisson structure, pseudo-Riemannian manifold

Abstract

Let $M$ be a differentiable manifold with a pseudo-Riemannian metric $g$ and a linear symmetric connection $K$. We deduce conditions to define Poisson or Jacobi structures on $TM$ for all vector fields and 2-vector fields naturally induced on $TM$ by $g$ and $K$.

Links

• GA201/99/0296, research and development project: Name: Diferenciální geometrie vyššího řádu

Investor: Czech Science Foundation, Differential geometry of higher order

• MSM 143100009, plan (intention): Name: Matematické struktury algebry a geometrie

Investor: Ministry of Education, Youth and Sports of the CR, Mathematical structures of algebra and geometry