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A class of Kaehler Einstein structures on the cotangent bundle | | Vasile Oproiu
; Dumitru Daniel Porosniuc
; | | Date: |
14 May 2004 | | Subject: | Differential Geometry MSC-class: 53C07, 53C15, 53C55 | math.DG | | Abstract: | We use some natural lifts defined on the cotangent bundle T*M of a Riemannian manifold (M,g) in order to construct an almost Hermitian structure (G,J) of diagonal type. The obtained almost complex structure J on T*M is integrable if and only if the base manifold has constant sectional curvature and the coefficients as well as their derivatives, involved in its definition, do fulfill a certain algebraic relation. Next one obtains the condition that must be fulfilled in the case where the obtained almost Hermitian structure is almost Kaehlerian. Combining the obtained results we get a family of Kaehlerian structures on T*M, depending on two essential parameters. Next we study three conditions under which the considered Kaehlerian structures are Einstein. In one of the obtained cases we get that (T*M,G,J) has constant holomorphic curvature. | | Source: | arXiv, math.DG/0405277 | | Services: | Forum | Review | PDF | Favorites | |
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