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A Kaehler Einstein structure on the cotangent bundle of a Riemannian manifold | | Vasile Oproiu
; Dumitru Daniel Porosniuc
; | | Date: |
15 Aug 2003 | | Journal: | An. St. Univ. " Al.I.Cuza " Iasi, 49 (2003), s.I a, Matematica, f2, 399-414 | | Subject: | Differential Geometry MSC-class: 53C07, 53C15, 53C55 | math.DG | | Abstract: | We use the natural lifts of the fundamental tensor field g to the cotangent bundle T*M of a Riemannian manifold (M,g), in order to construct an almost Hermitian structure (G,J) of diagonal type on T*M. The obtained almost complex structure J on T*M is integrable if and only if the base manifold has constant sectional curvature and the second coefficient, involved in its definition is expressed as a rational function of the first coefficient and its first order derivative. Next one shows that the obtained almost Hermitian structure is almost Kaehlerian. Combining the obtained results we get a family of Kaehlerian structures on T*M, depending on one essential parameter. Next we study the conditions under which the considered Kaehlerian structure is Einstein. In this case (T*M,G,J) has constant holomorphic curvature. | | Source: | arXiv, math.DG/0308149 | | Services: | Forum | Review | PDF | Favorites | |
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