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In this paper, we study the doubly warped product manifolds with semisymmetric metric connection. We derive the curvatures formulas for doubly warped product manifold with semi-symmetric metric connection in terms of curvatures of…
This study aims mainly at investigating the effects of concircular flatness and concircular symmetry of a warped product manifold on its fibre and base manifolds. Concircularly flat and concircularly symmetric warped product manifolds are…
We provide conditions under which an isometric immersion of a (warped) product of manifolds into a space form must be a (warped) product of isometric immersions.
The following problem is addressed: A $3$-manifold $M$ is endowed with a triple $\Omega = \big(\Omega^1,\Omega^2,\Omega^3\big)$ of closed $2$-forms. One wants to construct a coframing $\omega = \big(\omega^1,\omega^2,\omega^3\big)$ of $M$…
In this paper we study warped-product metrics on manifolds of the form $X \setminus Y$, where $X$ denotes either $\mathbb{H}^n$ or $\mathbb{C} \mathbb{H}^n$, and $Y$ is a totally geodesic submanifold with arbitrary codimension. The main…
In this paper, we prove a dihedral extremality and rigidity theorem for a large class of codimension zero submanifolds with polyhedral boundary in warped product manifolds. We remark that the spaces considered in this paper are not…
We study biwarped product submanifolds which are special cases of multiply warped product submanifolds in K\"{a}hler manifolds. We observe the non-existence of such submanifolds under some circumstances. We show that there exists a…
We study the $(2+2)$-Einstein warped product manifolds, where the scalar curvature of the Base is a multiple of the warping function, and we called this condition (inside a warped product manifold) $f$-curvature-Base ($R_{f_B}$).The aim of…
In this paper, we study semi-slant submanifolds and their warped products in Kenmotsu manifolds. The existence of such warped products in Kenmotsu manifolds is shown by an example and a characterization. A sharp relation is obtained as a…
We study conformal product structures on compact reducible Riemannian manifolds, and show that under a suitable technical assumption, the underlying Riemannian mani\-folds are either conformally flat, or triple products, \emph{i.e.} locally…
In this paper we study warped product Einstein metrics over spaces with constant scalar curvature. We call such a manifold rigid if the universal cover of the base is Einstein or is isometric to a product of Einstein manifolds. When the…
The object of the present paper is to study the characterization of warped product manifolds satisfying some pseudosymmetric type conditions, especially, due to projective curvature tensor. For this purpose we consider a warped product…
In this paper we review $G_2$ and $Spin(7)$ geometries in relation with a special type of metric structure which we call warped-like product metric. We present a general ansatz of warped-like product metric as a definition of warped-like…
This paper has two goals; the first is to generalize results for the existence and nonexistence of warped product submanifolds of almost contact manifolds, accordingly a self-contained reference of such submanifolds is offered to save…
This paper completes a fundamental construction in Alexandrov geometry. Previously we gave a new construction of metric spaces with curvature bounds either above or below, namely warped products with intrinsic metric space base and fiber,…
The decomposability of a Cartesian product of two nondecomposable manifolds into products of lower dimensional manifolds is studied. For 3-manifolds we obtain an analog of a result due to Borsuk for surfaces, and in higher dimensions we…
We prove some isoperimetric type inequalities in warped product manifolds, or more generally, multiply warped product manifolds. We then relate them to inequalities involving the higher order mean-curvature integrals. We also apply our…
We investigate manifolds obtained as a quotient of a doubly warped product. We show that they are always covered by the product of two suitable leaves. This allows us to prove, under regularity hypothesis, that these manifolds are a doubly…
We show that an asymptotically flat Riemannian three-manifold with non-negative scalar curvature is isometric to flat $\mathbb{R}^3$ if it admits an unbounded area-minimizing surface. This answers a question of R. Schoen.
In this paper, we study the existence of proper warped product submanifolds in metallic (or Golden) Riemannian manifolds and we discuss about semi-invariant, semi-slant and, respectively, hemi-slant warped product submanifolds in metallic…