TY - JOUR ID - 2132 TI - Regarding the Kähler-Einstein structure on Cartan spaces with Berwald connection JO - Iranian Journal of Science JA - ISTT LA - en SN - 2731-8095 AU - Peyghan, E. AU - Ahmadi, A. AU - Tayebi, A. AD - Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran AD - Department of Mathematics and Computer Science, Qom University, Qom, Iran Y1 - 2011 PY - 2011 VL - 35 IS - 2 SP - 89 EP - 99 KW - Cartan space KW - Kähler structure KW - symmetric space KW - Einstein manifold KW - Laplace operator KW - Divergence KW - Gradient DO - 10.22099/ijsts.2011.2132 N2 - A Cartan manifold is a smooth manifold M whose slit cotangent bundle 0T *M is endowed with a regularHamiltonian 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 Riemannianone. UR - https://ijsts.shirazu.ac.ir/article_2132.html L1 - https://ijsts.shirazu.ac.ir/article_2132_4fa62841602c5c773b2e2a0608226987.pdf ER -