In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped product structure. We obtain a uniqueness result for prescribing the Ricci curvatur…
Characterizes metallic structures on product manifolds and provides conditions for warped products to be metallic.
problem Understanding metallic structures on product manifolds and conditions for warped products to be metallic.
method Characterization through metallic maps and necessary/sufficient conditions for warped products.
result Characterizes metallic structures and provides conditions for warped products to be metallic.
Warped product affects divergences in information geometry.
problem Warped product's impact on divergences in information geometry.
method Study of warped product on information geometry.
result Warped product does not preserve canonical divergences.
In this paper, we generalize the geometry of the product pseudo-Riemannian manifold equipped with the product Poisson structure (\cite{Nas2}) to the geometry of a warped product of pseudo-Riemannian manifolds equipped with a warped Poisson structure. We construct three bivector fields on a product manifold and show tha…
The paper studies Einstein-type structures in warped product manifolds.
problem Characterizing Einstein-type structures in warped product manifolds.
method Analyzing conditions for minimal, totally umbilical, and geodesic immersions.
result Characterization of rotational hypersurfaces in RimesfRn. The paper studies affine connections on singular warped products and their curvature.
problem Analyzing affine connections on singular warped products.
method Introducing semi-symmetric metric and non-metric Koszul forms, and expressing their curvature in terms of factor manifolds.
result Generalized results for singular multiply warped products.
Backward propagation rules for warped products under Ricci flow.
problem Understanding how warped product structures behave under Ricci flow.
method Establishing sufficient conditions for backward propagation of warped product structures.
result Asymptotically conical shrinkers are multiply-warped products over Einstein manifolds.
Study on warped product Yamabe solitons with constant fiber curvature.
problem Characterizing nontrivial warped product Yamabe gradient solitons.
method Investigation of warped product manifolds, derivation of scalar curvature estimates.
result Nontrivial warped product Yamabe gradient solitons have constant scalar curvature in the fiber.
Study new warped product metric in contact geometry.
problem Define a new type warped product metric.
method Introduced a new warped product metric on product manifolds.
result Showed existence of α-Sasakian structure. The paper explores warped-like product metrics with exceptional holonomy groups.
problem Exploring new metrics with exceptional holonomy groups.
method Presented a general ansatz of warped-like product metric and studied specific examples.
result Explicit examples of (3+3+2) and (3+3+1) warped-like product manifolds with Spin(7) and G2 holonomy, respectively. We prove that complete warped product Einstein metrics with isometric bases, simply connected space form fibers, and the same Ricci curvature and dimension are isometric. In the compact case we also prove that the warping functions must be the same up to scaling, while in the non-compact case there are simple examples …
The paper explores geometric properties of Riemannian warped product maps and their curvature.
problem Investigating the geometric properties of Riemannian warped product maps.
method The approach involves establishing conditions for geodesics, deriving curvature tensors, and examining various types of maps.
result Derivation of integral formula for scalar curvature of conformal Riemannian warped product maps.
Study Einstein warped products with Einstein base and fiber.
problem Characterize Einstein warped products with Einstein base and fiber.
method Investigate necessary and sufficient conditions for a warped product to be Einstein.
result Explicitly determine the warping function when the base is hyperbolic space.
The paper extends affine connection results to singular warped and twisted products.
problem Generalizing affine connections to singular warped and twisted products.
method Study of singular multiply warped products and singular twisted products with semi-symmetric metric and non-metric connections, discussing Koszul forms and curvature.
result Theoretical results on curvature and Koszul forms for singular multiply warped and twisted products.
The paper characterizes warped product submanifolds in LCS-manifolds.
problem Characterizing warped product submanifolds in LCS-manifolds.
method Analyzing contact CR-warped product and pseudo-slant submanifolds, and constructing examples.
result There do not exist any proper warped product bi-slant submanifolds of LCS-manifolds.
In this paper, we generalize the dualistic structures on warped product manifolds to the dualistic structures on generalized warped product manifolds. we develop an expression of curvature for the connection of the generalized warped product in relation to those corresponding analogues of its base and fiber and warping…
In the present paper, we study warped product semi-slant submanifolds of Kenmotsu manifolds. We have obtained results on the existence of warped product semi-slant submanifolds of Kenmotsu manifolds in term of the canonical structure .
Study on Ricci-Bourguignon solitons on specific product spaces.
problem Characterizing Ricci-Bourguignon solitons on sequential warped products.
method Obtained necessary conditions for solitons to be Einstein manifolds under specific potential fields.
result Conditions for Ricci-Bourguignon solitons to be Einstein are identified.
The object of the present paper is to obtain the characterization of a warped product semi-Riemannian manifold with a special type of recurrent like structure, called super generalized recurrent. As consequence of this result we also find out the necessary and sufficient conditions for a warped product manifold to sati…
In this paper, we introduce horizontal and vertical warped product Finsler manifold. We prove that every C-reducible or proper Berwaldian doubly warped product Finsler manifold is Riemannian. Then, we find the relation between Riemmanian curvatures of doubly warped product Finsler manifold and its components, and consi…
The present article provides a study of 2−Killing vector fields on warped product manifolds as well as characterization of this structure on standard static and generalized Robertson-Walker space-times. Some conditions for a 2−Killing vector field on a warped product manifold to be parallel are obtained. Moreover, …
Characterizes certain Kähler manifolds with doubly-warped product structures.
problem Understanding Kähler manifolds with specific geometric properties.
method Obata-type characterization for Kähler manifolds with doubly-warped product structures.
result Complete description of Kähler doubly-warped product structures with Einstein metrics.
The paper classifies Einstein warped product manifolds with specific properties.
problem Characterizing Einstein warped product semi-Riemannian manifolds.
method Analyzing a class of Einstein warped product manifolds with specific conditions.
result Proves that certain Einstein warped product manifolds are simply Riemannian products.
Study classifies Einstein spaces and warped products in weighted geometry.
problem Characterizing geometric structures of weighted Einstein spaces.
method Complete local classification of weighted Einstein spaces with harmonic Weyl tensor.
result Spaces decompose into Einstein or specific warped products.
We characterize Osserman and conformally Osserman Riemannian manifolds with the local structure of a warped product. By means of this approach we analyze the twisted product structure and obtain, as a consequence, that the only Osserman manifolds which can be written as a twisted product are those of constant curvature…
The study proves conditions for quasi-Einstein manifolds with specific structures to be Einstein.
problem Conditions for quasi-Einstein manifolds to have Einstein structures.
method Proved conditions for quasi-Einstein semi-Riemannian warped products to have Einstein fibers.
result Found conditions for quasi-Einstein manifolds with specific structures to be Einstein.
Absolute index theorem for warped product manifolds.
problem Equivariant index computation for manifolds with warped product structures.
method Warped product structure, Fredholm operator, Atiyah-Segal-Singer index theorem.
result Equivariant relative index theorem for manifolds with warped product structures.
The paper studies gradient Ricci-Harmonic solitons on warped product manifolds.
problem Characterizing gradient Ricci-Harmonic solitons on warped product manifolds.
method Warped product structure, potential function, warping function, harmonic map analysis.
result Nontrivial examples of warped product gradient Ricci-harmonic solitons are provided.
The paper studies a flow on warped G2-structures, providing conditions for existence and describing new solutions.
problem Analyzing the Laplacian coflow on warped G2-structures.
method Explicit reinterpretation of the flow as differential form equations and warping function conditions.
result New long-time solutions for nearly Kähler, symplectic half-flat, and balanced SU(3)-structures.
Study of Laplacian flow on warped G2-manifolds.
problem Evolution of G2-structures on warped products.
method Interpreting flow as equations on base manifold, finding conditions for solutions.
result Construction of immortal solutions and new examples of solitons.
Study biharmonic submanifolds in warped product structures.
problem Characterize biharmonic submanifolds in warped product spaces.
method Analyze tension and bitension fields, relate to warping function and geometry of submanifolds.
result Characterize tangentially and normally biharmonic cases via differential conditions on the warping function.
Study on special symmetries in biwarped product 3-manifolds.
problem Characterizing Killing vector fields on biwarped product-type 3-manifolds.
method Derived system of equations for Killing fields and described their structure.
result Families of solutions found, including explicit examples.
The study classifies totally umbilical surfaces in warped product manifolds.
problem Classifying totally umbilical surfaces in warped product manifolds.
method Analyzing surfaces in warped product M(κ)fimesI and finding first integrals. result Totally umbilical surfaces in M(κ)fimesI are invariant by isometries. The article surveys recent results on warped and CR-warped product submanifolds in Kaehler manifolds.
problem Characterizing submanifolds in Kaehler manifolds using warped and CR-warped products.
method Analyzing properties of warped and CR-warped products in the context of Kaehler manifolds.
result Presented several results on the geometry of warped and CR-warped product submanifolds.
The paper examines Einstein doubly warped product manifolds with a semi-symmetric metric connection.
problem Characterizing Einstein doubly warped product manifolds with a semi-symmetric metric connection.
method Deriving curvature formulas and proving necessary and sufficient conditions for a manifold to be a warped product.
result Obtained results for Einstein doubly warped product manifolds and Einstein-like doubly warped product manifolds.
Generalizes warped product submersion to conformal case.
problem Understanding angles preservation in submersions.
method Introduces conformal warped product submersion.
result Fundamental tensors derived for conformal submersion.
The paper explores null distance convergence for warped product spacetimes.
problem Defining convergence for sequences of spacetimes as metric spaces.
method Using the null distance to define convergence of spacetimes.
result Optimal convergence theorem for warped product spacetimes.
In this paper, we investigate the condition on warped product manifold of a Kenmotsu manifold and the real line to be a conformal Kahler manifold. This result demonstrates the close relation of Kenmotsu and Kahler manifolds.
We consider surfaces with constant mean curvature in certain warped product manifolds. We show that any such surface is umbilic, provided that the warping factor satisfies certain structure conditions. This theorem can be viewed as a generalization of the classical Alexandrov theorem in Euclidean space. In particular, …
The paper studies isoperimetric inequalities on warped product manifolds.
problem Investigating isoperimetric inequalities on warped product manifolds.
method Exploiting the interplay between isoperimetric inequalities and warped product structures, deriving necessary and sufficient conditions.
result Established a quantitative lower bound for the first nonzero Dirichlet eigenvalue of geodesic balls centered at the pole.
The paper introduces and studies a new type of submersion in Riemannian geometry.
problem Exploring new submersions in Riemannian geometry.
method Defining and studying Clairaut Riemannian warped product submersions.
result Established conditions for a Riemannian warped product submersion to satisfy the Clairaut condition.
Proves a theorem for a specific type of warped product space.
problem Analyzing warped product spaces.
method Uses the warped function \( f(r) = \cosh\left(r\sqrt{\frac{\lambda}{n-2}}
ight) \) to prove the theorem.
result Proves an almost splitting theorem for the specified warped product space.
Using as an underlying manifold an alpha-Sasakian manifold we introduce warped product Kaehler manifolds. We prove that if the underlying manifold is an alpha-Sasakian space form, then the corresponding Kaehler manifold is of quasi-constant holomorphic sectional curvatures with special distribution. Conversely, we prov…
The paper proves rigidity for submanifolds in warped product manifolds.
problem Rigidity of submanifolds in warped product manifolds.
method Dihedral extremality and rigidity theorem for submanifolds with polyhedral boundary.
result Dihedral rigidity results for hyperbolic polyhedra in flat warped product spaces.
We show a geometric rigidity of isometric actions of non compact (semisimple) Lie groups on Lorentz manifolds. Namely, we show that the manifold has a warped product structure of a Lorentz manifold with constant curvature by a Riemannian manifold.
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 warped product up to a zero measure subset formed by an union of leaves. We also…
Paper defines and studies Clairaut warped product Riemannian maps.
problem Understanding the geometry of specific Riemannian maps.
method Identify geodesic conditions, derive conditions for Clairaut maps, and calculate curvature.
result Found conditions for a warped product Riemannian map to be Clairaut.
Study on warped product pointwise semi-slant submanifolds in Sasakian and cosymplectic manifolds.
problem Investigate the geometry of pointwise semi-slant submanifolds and their warped products.
method Using the notion of pointwise slant submanifolds, investigate the geometry of pointwise semi-slant submanifolds and their warped products in Sasakian and cosymplectic manifolds.
result Prove the existence of no proper pointwise semi-slant warped product submanifolds other than contact CR-warped products in Sasakian manifolds.