2010/04/06 by E. Peyghan, A. Tayebi, Akbar Tayebi +5 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph) #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1004.0796
This article is in 15 page. arXiv admin note: text overlap with this http URL and arXiv:1202.6202 by other author
arxiv created 2010/04/06 · openalex publication_date 2010/04/06 · arxiv updated 2012/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Cartan manifold is a smooth manifold M whose slit cotangent bundle T*M0 is endowed with a regular Hamiltonian K which is positively homogeneous of degree 2 in momenta. The Hamiltonian K defines a (pseudo)-Riemannian metric gij in the vertical bundle over T*M0 and using it a Sasaki type metric on T*M0 is constructed. A natural almost complex structure is also defined by K on T*M0 in such a way that pairing it with the Sasaki type metric an almost Kähler structure is obtained. In this paper we deform gij to a pseudo-Riemannian metric Gij and we define a corresponding almost complex Kähler structure. We determine the Levi-Civita connection of G and compute all the components of its curvature. Then we prove that if the structure (T*M0, G, J) is Kähler- Einstein, then the Cartan structure given by K reduce to a Riemannian one.