arXiv subjects

Vasile Oproiu

Publications and source records attributed to Vasile Oproiu.

2 recordsLinked to original sources

arXiv2004

A class of Kaehler Einstein structures on the cotangent bundle

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.

math.DG↗

arXiv2003

A Kaehler Einstein structure on the cotangent bundle of a Riemannian manifold

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.

math.DG↗