Abstract.
In [11] we have considered a family of natural almost anti-Hermitian structures (G, J) on the tangent bundle TM of a Riemannian manifold (M, g), where the semi-Riemannian metric G is a lift of natural type of g to TM, such that the vertical and horizontal distributions VTM, HTM are maximally isotropic and the almost complex structure J is a usual natural lift of g of diagonal type interchanging VTM, HTM (see [5], [15]). We have obtained the conditions under which this almost anti-Hermitian structure belongs to one of the eight classes of anti-Hermitian manifolds obtained in the classification given in [1]. In this paper we consider another semi-Riemannian metric G on TM such that the vertical and horizontal distributions are orthogonal to each other. We study the conditions under which the above almost complex structure J defines, together with G, an almost anti-Hermitian structure on TM. Next, we obtain the conditions under which this structure belongs to one of the eight classes of anti-Hermitian manifolds obtained in the classification in [1].
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Partially supported by the Grant 100/2003, MECT-CNCSIS, România.
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Oproiu, V., Papaghiuc, N. Some Classes of Almost Anti-Hermitian Structures on the Tangent Bundle. MedJM 1, 269–282 (2004). https://doi.org/10.1007/s00009-004-0015-5
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DOI: https://doi.org/10.1007/s00009-004-0015-5