Showing papers by "David E. Blair published in 2016"
TL;DR: In this paper, a 3D conformally flat almost contact metric manifold with non-constant sectional curvature was constructed and the curvature properties of the manifold were investigated.
Abstract: In this paper, we first focus on conformally flat almost $${C(\alpha)}$$
-manifolds. Moreover, we construct an example of a 3-dimensional conformally flat almost $${\alpha}$$
-Kenmotsu manifold which is of non-constant sectional curvature. By means of this example, we also illustrate a 3-dimensional conformally flat almost Kenmotsu manifold which not only contrasts with both H
3(−1) and $${H^{2}(-4)\times\mathbb{R}}$$
but also is of non-constant sectional curvature. Then, we study conformally flat, $${\phi}$$
-RK contact metric and almost contact metric manifolds. Next, we investigate the curvature properties of conformally flat generalized Sasakian space forms. Finally, we deal with conformally flat almost contact metric manifolds which are *-
$${\eta}$$
-Einstein. In this regard, we are also interested in conformally flat contact metric manifolds of $${{\rm dim}{\geq}5}$$
which are *-
$${\eta}$$
-Einstein.
4 citations
TL;DR: In this paper, the authors show that a g-natural almost Hermitian structure is Bochner flat if and only if it is conformally equivalent to the Sasaki metric on the tangent bundle of a Riemannian manifold.
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.