2004/05/14 by Vasile Oproiu, Oproiu, Vasile, Dumitru Daniel Porosniuc +1
Mathematics · #53C07 #53C15 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C07 #msc:53C15 #msc:53C55
paper · pdf · doi:10.48550/arxiv.math/0405277
21 pages, LaTeX2e, to appear in "Publicationes Matheticae", Debrecen
arxiv created 2004/05/14 · arxiv updated 2009/12/01
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.