S-Manifolds Versus Indefinite S-Manifolds and Local Decomposition Theorems

Abstract

To any globally framed f-manifold carrying a structure of S-manifold we associate several indefinite S-manifolds. We determine the links between the corresponding Levi-Civita connections and sectional curvatures. We state some local semi-Riemannian decomposition theorems.

Characteristics of Sasakian Manifolds Admitting Almost ∗-Ricci Solitons

“…Only one new tensor N (5) (vanishing at Q = 0), which supplements the sequence of well-known tensors N (i) , i = 1, 2, 3, 4, is needed to study the weak f -contact structure. For particular values of the tensor N (5) we get…”

“…A metric f -structure on a (2n + s)-dimensional smooth manifold is a higher dimensional analog of a contact structure, defined by a (1,1)-tensor f of constant rank 2n, which satisfies f 3 +f = 0, and orthonormal vector fields {ξ i } 1≤i≤s spanning ker f -the 2n-dimensional characteristic distribution, see [4,5,14,31,32,33]. Foliations of simple extrinsic geometry, i.e., vanishing second fundamental form of the leaves, appear on manifolds with degenerate differential forms and curvature-like tensors, e.g.…”

On the Splitting Tensor of the Weak f-Contact Structure

“…In [17], conditions are found under which a given compact f -K-contact manifold is a mapping torus of such a manifold of lower dimension. Various symmetries of contact and framed f -manifolds are studied, e.g., in [18], and sufficient conditions are considered when an f -contact manifold carries a canonical metric, such as Einstein-type or constant curvature, or admits a local decomposition (splitting), in [4,19,20].…”

Geometry of Warped Product Hemi-Slant Submanifolds of an S-Manifold

“…For s ≥ 2, examples of an S-manifold are presented in [3][4][5][6]. Furthermore, an S-manifold has been studied by several authors (see, for example, [2,[7][8][9][10]).…”