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Regarding the Kähler-Einstein structure on Cartan spaces with Berwald connection | ||
| Iranian Journal of Science | ||
| مقاله 3، دوره 35، شماره 2، مرداد 2011، صفحه 89-99 اصل مقاله (174.87 K) | ||
| نوع مقاله: Regular Paper | ||
| شناسه دیجیتال (DOI): 10.22099/ijsts.2011.2132 | ||
| نویسندگان | ||
| E. Peyghan* 1؛ A. Ahmadi1؛ A. Tayebi2 | ||
| 1Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran | ||
| 2Department of Mathematics and Computer Science, Qom University, Qom, Iran | ||
| چکیده | ||
| A Cartan manifold is a smooth manifold M whose slit cotangent bundle 0 T *M is endowed with a regular Hamiltonian K which is positively homogeneous of degree 2 in momenta. The Hamiltonian K defines a (pseudo)-Riemannian metric ij g in the vertical bundle over 0 T *M and using it, a Sasaki type metric on 0 T *M is constructed. A natural almost complex structure is also defined by K on 0 T *M in such a way that pairing it with the Sasaki type metric an almost Kähler structure is obtained. In this paper we deform ij g to a pseudo-Riemannian metric ij G 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 ( , , ) 0 T *M G J is Kähler- Einstein, then the Cartan structure given by K reduces to a Riemannian one. | ||
| کلیدواژهها | ||
| Cartan space؛ Kähler structure؛ symmetric space؛ Einstein manifold؛ Laplace operator؛ Divergence؛ Gradient | ||
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