Integrable geodesic flows and super polytropic gas equations

✍ Scribed by Partha Guha

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 95 KB
• Volume: 46
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(02)00123-7

✦ Synopsis

The polytropic gas equations are shown to be the geodesic flows with respect to an L 2 metric on the semidirect product space Diff(S 1 ) C ∞ (S 1 ), where Diff(S 1 ) is the group of orientation preserving diffeomorphisms of the circle. We also show that the N = 1 supersymmetric polytropic gas equation constitute an integrable geodesic flow on the extended Neveu-Schwarz space. Recently other kinds of supersymmetrizations have been studied vigorously in connection with superstring theory and are called supersymmetric-B (SUSY-B) extension. In this paper we also show that the SUSY-B extension of the polytropic gas equation form a geodesic flow on the extension of the Neveu-Schwarz space.