Abstract:
We present some aspects from the study of geometric structures of
natural lift type on the tangent bundle of a Riemannian manifold.
After presenting, in the first two sections, the basic constructions
leading to the almost Hermitian structures of diagonal type, we find
the conditions under which such structures are almost Kählerian or
Kählerian. In section 4 we present the results concerning the
almost anti-Hermitian structures. Next we study the
general natural almost Hermitian structures, obtaining similar
results. Finally, in section 6 we obtain sufficient conditions for a
general natural Kaehler structure on the tangent bundle to be a
Kaehler Einstein structure.
Key Words: tangent bundle, Riemannian metric, general natural lift, Einstein
structure.
2000 Mathematics Subject Classification: Primary: 53C55,
Secondary: 53C15, 53C05.
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