REGARDING THE KAHLER-EINSTEIN STRUCTURE ON CARTAN SPACES WITH BERWALD CONNECTION

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PEYGHAN E.; AHMADI A.; TAYEBI A.

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Journal: Iranian Journal of Science Year:2011 | Volume:35 | Issue:A2 Page(s): 89-99

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Title

REGARDING THE KAHLER-EINSTEIN STRUCTURE ON CARTAN SPACES WITH BERWALD CONNECTION

Author(s)

PEYGHAN E. | AHMADI A. | TAYEBI A. | Issue Writer Certificate

Keywords

CARTAN SPACE

KAHLER STRUCTURE

SYMMETRIC SPACE

EINSTEIN MANIFOLD

LAPLACE OPERATOR

DIVERGENCE

GRADIENT

Abstract

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 KAHLER STRUCTURE is obtained. In this paper we deform Gij to a pseudo-Riemannian metric Gij and we define a corresponding almost complex KAHLER 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 Kahler-Einstein, then the Cartan structure given by K reduces to a Riemannian one.

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APA: Copy

PEYGHAN, E., AHMADI, A., & TAYEBI, A.. (2011). REGARDING THE KAHLER-EINSTEIN STRUCTURE ON CARTAN SPACES WITH BERWALD CONNECTION. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE, 35(A2), 89-99. SID. https://sid.ir/paper/581319/en

Vancouver: Copy

PEYGHAN E., AHMADI A., TAYEBI A.. REGARDING THE KAHLER-EINSTEIN STRUCTURE ON CARTAN SPACES WITH BERWALD CONNECTION. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE[Internet]. 2011;35(A2):89-99. Available from: https://sid.ir/paper/581319/en

IEEE: Copy

E. PEYGHAN, A. AHMADI, and A. TAYEBI, “REGARDING THE KAHLER-EINSTEIN STRUCTURE ON CARTAN SPACES WITH BERWALD CONNECTION,” IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A- SCIENCE, vol. 35, no. A2, pp. 89–99, 2011, [Online]. Available: https://sid.ir/paper/581319/en

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