arXiv research

B.-Y. Chen initiated the study of warped product submanifolds in his fundamental seminal papers \cite{C1,C2,C2.1}. In this paper, we study contact CR-warped product submanifolds of cosymplectic space forms and prove an optimal inequality by using Gauss and Codazzi equations. In addition, we obtain two geometric inequal…

The paper proves a new inequality for CR-warped product submanifolds in complex space forms.

The warped product $N_1\times_f N_2$ of two Riemannian manifolds $(N_1,g_1)$ and $(N_2,g_2)$ is the product manifold $N_1\times N_2$ equipped with the warped product metric $g=g_1+f^2 g_2$, where $f$ is a positive function on $N_1$. Warped products play very important roles in differential geometry as well as in physic…

In this paper, we study warped products of contact skew-CR submanifolds, called contact skew CR-warped products. We establish an inequality for the squared norm of the second fundamental form in terms of the warping function and the slant angle. The equality case in the statement of the inequality is investigated and s…

Recently, M. Atcken studied Contact CR-warped prod- uct submanifolds in cosymplectic space forms and established gen- eral sharp inequalities for CR-warped products in a cosymplectic manifold [1]. In the present paper, we obtain an inequality for the squared norm of the second fundamental form in terms of constant ?$φ$…

The paper studies geometric properties of a specific type of submanifolds in Kaehler manifolds.

n this paper, we obtain a geometric inequality between the length of the second fundamental form and the length of Lee form in terms of the warping function for a CR-warped product submanifold in a locally conformal Kaehler space form. The equality case is also investigated. Furthermore, the inequality is discussed for…

The paper derives inequalities for contact CR-warped product submanifolds in cosymplectic space forms.

Recently Hui et al. (\cite{HAP}, \cite{HAN}) studied contact CR-warped product submanifolds and also warped product pseudo-slant submanifolds of a $(LCS)_n$-manifold $\bar{M}$. In this paper we have studied the characterization for both these classes of warped product submanifolds. It is also shown that there do not ex…

Recently, B.-Y. Chen and O. J. Garay studied pointwise slant submanifolds of almost Hermitian manifolds. By using the notion of pointwise slant submanifolds, we investigate the geometry of pointwise semi-slant submanifolds and their warped products in Sasakian and cosymplectic manifolds. We prove that there exist no pr…

B. Y. Chen established sharp inequalities between certain Riemannian invariants and the squared mean curvature for submanifolds in real space form as well as in complex space form. In this paper we generalize Chen inequalities for submanifolds of Bochner Kaehler manifolds. Moreover, we consider CR-warped product subman…

In the present paper, we study globally framed f-manifolds in the particular setting of indefinite S-manifolds for both spacelike and timelike cases. We prove that if $M = N^{\perp} \times_f N^T$ is a warped CR-submanifold such that $N^{\perp}$ is $φ$?-anti-invariant and NT is $φ$?-invariant, then M is a CR-product. We…

Paper explores existence and nonexistence of submanifolds in contact geometry.

The CR $δ$-invariant for CR-submanifolds was introduced in a recent article [B. Y. Chen, An optimal inequality for CR-warped products in complex space forms involving CR $δ$-invariant, Internat. J. Math. 23} (2012), no. 3, 1250045 (17 pages)]. In this paper, we prove two new optimal inequalities for anti-holomorphic su…

The paper studies a new type of submanifolds in product spaces.

The paper extends affine connection results to singular warped and twisted products.

Defines products for fibered corners manifolds, generalizing resolutions.

Productivity and credit limits affect aggregate production in non-monotonic ways.

Einstein metrics on products are shown to be warped.

Uniform criterion for vanishing products in bounded cohomology.

The paper studies affine connections on singular warped products and their curvature.

We refine the intersection product in homology to an equivariant setting, which unifies several known constructions. As an application, we give a common generalisation of the Chas-Sullivan string product on a manifold and the Chataur-Menichi string product on the classifying space by defining a string product on the Bo…

New method compares geometric and standard cup products.

The paper examines Einstein doubly warped product manifolds with a semi-symmetric metric connection.

Generalizes warped product submersion to conformal case.

The paper explores geometric properties of Riemannian warped product maps and their curvature.

In this article we obtain classification results on the quasi-product production functions in terms of the geometry of their associated graph hypersurfaces, generalizing in a new setting some recent results concerning basic production models. In particular, we obtain several results on the geometry of Spillman-Mitscher…

Constructing a conformal product structure on $S^3$ using the Reeb foliation.

The paper defines and analyzes curvature tensors on super twisted product spaces.

The study examines Einstein-Finsler spaces using Minkowskian products.

In this paper, we completely classify homogeneous production functions with an arbitrary number of inputs whose production hypersurfaces are flat. As an immediate consequence, we obtain a complete classification of homogeneous production functions with two inputs whose production surfaces are developable.

Study on warped product Yamabe solitons with constant fiber curvature.

Economies grow by upgrading the type of products they produce and export. The technology, capital, institutions and skills needed to make such new products are more easily adapted from some products than others. We study the network of relatedness between products, or product space, finding that most upscale products a…

A Riemannian almost product manifold with integrable almost product structure is called a Riemannian product manifold. In the present paper the natural connections on such manifolds are studied, i.e. the linear connections preserving the almost product structure and the Riemannian metric.

A new method for analyzing product competition using low-dimensional embeddings.

The study characterizes submanifolds in product spaces.

Paper reinterprets marginal productivity theory using vectorial products, challenging traditional ethical interpretations.

We introduce polar metrics on a product manifold, which have product and warped product metrics as special cases. We prove a de Rham-type theorem characterizing Riemannian manifolds that can be locally decomposed as a product manifold endowed with a polar metric. For a product manifold endowed with a polar metric, our …

Warped product affects divergences in information geometry.

Complementary products recommendation is an important problem in e-commerce. Such recommendations increase the average order price and the number of products in baskets. Complementary products are typically inferred from basket data. In this study, we propose the BB2vec model. The BB2vec model learns vector representat…

Study describes conformal product structures on compact Kähler manifolds.

A production function is a mathematical formalization in economics which denotes the relations between the output generated by a firm, an industry or an economy and the inputs that have been used in obtaining it. In this paper, we study the product production functions of 2 variables in terms of the geometry of their a…

The study restricts stable minimal immersions in product spaces to specific configurations.

Paper defines new submanifolds in Kaehler manifolds.

New interpretation reconciles country and product complexity.

Isoperimetric regions in scaled product manifolds are products of regions in each factor.

OMBA learns product and user representations for better online market basket analysis.

Groups with Property (T) have fiber products with Property (T).