Abstract
We consider g-natural metrics on the tangent bundle of a Riemannian manifold together with the almost complex structure which reverses the horizontal and vertical subspaces. This narrows the class of g-natural metrics to metrics conformally equivalent to the Sasaki metric on the tangent bundle with a restriction on the conformal factor. We then show that such a g-natural almost Hermitian structure is Bochner flat if and only if it is conformally equivalent to the Sasaki metric when the base manifold is flat and with the same restriction on the conformal factor.
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Acknowledgments
The second author expresses her appreciation to TUBITAK-BAYG for their financial support during her research at the Department of Mathematics of Michigan State University. She also expresses her appreciation to Professor David E. Blair for his kind invitation and to all the staff of the department for their hospitality.
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Blair, D.E., Yıldırım, H. Bochner flatness of tangent bundles with g-natural almost Hermitian metrics. Ann Glob Anal Geom 49, 259–269 (2016). https://doi.org/10.1007/s10455-015-9491-z
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DOI: https://doi.org/10.1007/s10455-015-9491-z