Study describes conformal product structures on compact Kähler manifolds.
problem Characterizing compact Kähler manifolds with conformal product structures.
method Geometric description of conformal product structures on compact Kähler manifolds.
result Geometric characterization of compact Kähler manifolds with conformal product structures.
Defined and proved monotonicity of a product on compact Hermitian manifolds.
problem Defining and proving properties of a product on compact Hermitian manifolds.
method Proved the well-definedness and monotonicity of the relative non-pluripolar product.
result Monotonicity of the relative non-pluripolar product in terms of masses on compact Hermitian manifolds.
No conformal product structures on compact manifolds with constant curvature.
problem Existence of conformal product structures on compact manifolds with constant curvature.
method Analyzing non-flat manifolds and irreducible, compact locally symmetric spaces of non-positive curvature.
result Compact non-flat manifolds with constant sectional curvature admit no conformal product structure.
Einstein metrics on products are shown to be warped.
problem Characterizing Einstein metrics on conformal products.
method Proving Einstein metrics on conformal products are warped products under natural geometric conditions.
result Einstein metrics on conformal products are proven to be warped products.
New result on Einstein manifolds using conformal product structures.
problem Understanding Einstein metrics on product manifolds.
method Generalizing previous results on Einstein metrics on product manifolds to conformal product structures.
result Einstein metrics on conformal product structures of compact manifolds are also warped product metrics.
The study restricts stable minimal immersions in product spaces to specific configurations.
problem Prohibiting stable minimal immersions in certain product spaces.
method Analyzing stable minimal immersions in products of complex, quaternionic, and octonionic projective spaces.
result The only stable compact minimal immersions in the product of a quaternionic projective space with any other Riemannian manifold are the products of quaternionic projective subspaces with compact stable minimal immersions of the second manifold.
Stable compact minimal submanifolds of the product of a sphere and any Riemannian manifold are classified whenever the dimension of the sphere is at least three. The complete classification of the stable compact minimal submanifolds of the product of two spheres is obtained. Also, it is proved that the only stable comp…
Nontrivial Massey products found on compact Kähler manifolds.
problem Understanding the cohomology structure of compact Kähler manifolds.
method Analyzing the bigraded quasi-isomorphism type of forms on compact Kähler manifolds.
result Nontrivial ABC-Massey products exist on compact Kähler manifolds, including on surfaces and higher-dimensional manifolds.
Products of LCK manifolds do not admit LCK structures.
problem Whether products of compact complex manifolds admit LCK metrics.
method Classifying known LCK manifolds and proving non-existence of LCK structures in product cases.
result Products of LCK manifolds do not admit LCK structures.
No proper biharmonic CMC compact hypersurface in a specific warped product space.
problem Existence of proper biharmonic CMC hypersurfaces in a warped product space.
method Finding necessary and sufficient conditions for proper biharmonic CMC hypersurfaces in a special warped product space.
result No proper biharmonic CMC compact hypersurface exists in the specified space.
Study on Riemannian Poisson warped product spaces and their properties.
problem Characterizing and understanding Riemannian Poisson warped product spaces.
method Formal treatment of Killing and 2-Killing 1-forms on Riemannian Poisson manifolds, including Bochner type results.
result Characterization of 2-Killing 1-form on (R2,g,Π) and Bochner type results on compact spaces. Study reveals vanishing Massey products on compact complex surfaces, impacting their fundamental group structure.
problem Understanding the real homotopy type of compact complex surfaces.
method Analyzes Massey products and fundamental group presentations, providing explicit presentations in non-Kähler cases.
result Explicit presentations of fundamental groups based on first Betti numbers, vanishing Massey products beyond certain lengths.
Study stability of operators on warped product manifolds.
problem Stability of operators on warped product manifolds.
method Examined the family of operators La=Δ−aS in a warped product of an infinite interval or real line by a compact manifold. result Stability of the operators La was studied in a specific type of manifold. 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 examines conditions for compactness in sequences of warped product length spaces.
problem Conditions for compactness in sequences of warped product length spaces.
method Analyzes conditions on warping functions for compactness and Lipschitz bounds.
result Necessary conditions for compactness and Lipschitz bounds are identified.
We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products of Kahler-Einstein manifolds. We compute the associated conformal invariants, i…
We study some similarities between almost product Riemannian structures and almost Hermitian structures. Inspired by the similarities, we prove lower eigenvalue estimates for the Dirac operator on compact Riemannian spin manifolds with locally product structures. We also provide some examples (limiting manifolds) for t…
The paper classifies compact hyperbolic Coxeter polytopes and improves upper bounds.
problem Classifying compact hyperbolic Coxeter polytopes and understanding their combinatorial properties.
method Study of imes0-products of Lannér diagrams, proving superhyperbolic properties, and analyzing Lannér subdiagrams. result Improved upper bounds on the dimension of compact hyperbolic Coxeter polytopes.
Let X be a Hausdorff topological group and G a locally compact subgroup of X. We show that X admits a locally finite σ-discrete G-functionally open cover each member of which is G-homeomorphic to a twisted product G×HSi, where H is a compact large subgroup of G (i.e., the quotient G/H is a…
Proves elliptic operator images are closed on Hilbert bundles.
problem Closedness of images of elliptic operators on Hilbert bundles.
method Analyzes tensor product of elliptic operators and compares images.
result Establishes closedness of images with respect to natural topology.
We study the geometry of compact Lorentzian manifolds that admit a somewhere timelike Killing vector field, and whose isometry group has infinitely many connected components. Up to a finite cover, such manifolds are products (or amalgamated products) of a flat Lorentzian torus and a compact Riemannian (resp., lightlike…
The study finds starshaped compact hypersurfaces in warped products with curvature estimates.
problem Finding starshaped compact hypersurfaces in warped product manifolds.
method Deriving global curvature estimates and interior second order a priori estimates for solutions to associated equations.
result Existence of starshaped compact hypersurfaces in warped product manifolds.
A product of Kähler manifolds also carries a Kähler metric. In this short note we would like to study the product of generalized p−Kähler manifolds, compact or not. The results we get extend the known results (balanced, SKT, sG manifolds), and are optimal in the compact case. Hence we can give new non-trivial example…
New rigidity result for convex co-compact actions in products of spaces.
problem Rigidity of convex co-compact actions in products of spaces.
method Analyzing diagonal actions and marked length spectra.
result If a diagonal action is convex co-compact, then the individual actions have the same marked length spectrum.
We show that a compact n-polyhedron PL embeds in a product of n trees if and only if it collapses onto an (n-1)-polyhedron. If the n-polyhedron is contractible and n\ne 3 (or n=3 and the Andrews-Curtis Conjecture holds), the product of trees may be assumed to collapse onto the image of the embedding. In contrast, there…
Paper studies Hessian quotient equations in warped product manifolds.
problem Analyzing Hessian quotient equations in warped product manifolds.
method Using standard degree theory and a priori estimates.
result Existence of star-shaped compact hypersurface solutions.
Study finds solutions for complex problems on non-compact manifolds.
problem Solving fully nonlinear Yamabe-type problems on non-compact manifolds.
method Existence results for a class of problems, considering both positive and negative cases.
result Explicit examples of manifolds satisfying the hypotheses of the theorems.
The study classifies quasi-Einstein manifolds with boundary.
problem Classifying quasi-Einstein manifolds with boundary.
method Analyzing scalar curvature and isometric properties.
result Compact quasi-Einstein manifolds with boundary are rigid.
We study twistor forms on products of compact Riemannian manifolds and show that they are defined by Killing forms on the factors. The main result of this note is a necessary step in the classification of compact Riemannian manifolds with non-generic holonomy carrying twistor forms.
We investigate some topological properties, in particular formality, of compact Sasakian manifolds. Answering some questions raised by Boyer and Galicki, we prove that all higher (than three) Massey products on any compact Sasakian manifold vanish. Hence, higher Massey products do obstruct Sasakian structures. Using th…
Killing tensors on reducible spaces are reducible, except for special cases.
problem Characterizing Killing tensors on reducible spaces.
method Analyzing Killing tensors on product manifolds and their lifts.
result Killing tensors on product manifolds are reducible, except for specific cases.
The study proves uniqueness and symmetry of self-similar solutions in warped product spaces.
problem Uniqueness and symmetry of self-similar solutions in warped product spaces.
method Analysis of curvature flows with homogeneous speed functions in warped product spaces.
result Compact star-shaped self-similar solutions in warped product spaces are slices.
Locally conformally product Lie algebras are characterized and constructed.
problem Characterizing and constructing compact locally conformally product Lie algebras.
method Characterization via closed 1-forms and non-unimodular Lie algebras acting on abelian ones.
result Explicit examples of compact LCP manifolds that are not solvmanifolds.
Constructing a conformal product structure on S3 using the Reeb foliation.
problem First example of conformal product structure on compact simply connected manifold.
method Reeb foliation
result Conformal product structure on S3 In the first part of this note we study compact Riemannian manifolds (M,g) whose Riemannian product with R is conformally Einstein. We then consider compact 6--dimensional almost Hermitian manifolds of type W_1+W_4 in the Gray--Hervella classification admitting a parallel vector field and show that (under some regulari…
Estimates heights of special surfaces in warped products.
problem Estimating heights of special surfaces in warped products.
method Provided a vertical height estimate.
result Vertical height estimates for special Weingarten surfaces of elliptic type in warped products.
The study classifies stable submanifolds in product spaces of projective spaces.
problem Classifying stable submanifolds in product spaces of projective spaces.
method Provided a classification theorem for compact stable minimal immersions in product spaces of projective spaces.
result Characterized complex minimal immersions in the product of two complex projective spaces.
Non-formal G2 manifold found with holonomy.
problem Existence of non-formal G2 manifolds.
method Construction method of compact torsion-free G2 manifolds.
result Found a compact, simply connected G2 manifold that is non-formal.
The study proves a theorem on Riemannian manifolds for wedge products of weakly convergent differential forms.
problem Analyzing the limiting behavior of wedge products of weakly convergent differential forms on Riemannian manifolds.
method Formulating and proving compensated compactness theorems for wedge products of differential forms on closed Riemannian manifolds.
result The theorem generalizes the div-curl lemma for vectorfields and applies to critical regularity exponents.
The paper proves compactness of warped product metrics on S²×S¹ with varying base metrics.
problem Proving compactness of warped product metrics on S²×S¹ with nonnegative scalar curvature.
method Using Gromov-Sormani MinA scalar curvature compactness conjecture, the paper proves a uniform diameter bound for the base surfaces, compactness of the base warping functions, and convergence of the metrics.
result The metrics converge to a limit metric with nonnegative scalar curvature in the distributional sense.
Study compact sequences of warped product circles over spheres with nonnegative scalar curvature.
problem Compactness of sequences of warped product circles over spheres with nonnegative scalar curvature.
method Proved subsequence convergence to a W1,p Riemannian metric for all p<2 with nonnegative scalar curvature in the distributional sense. result Proved compactness of sequences of warped product circles over spheres with nonnegative scalar curvature.
We give a necessary and sufficient condition for orbits of commutative Hermann actions and actions of the direct product of two symmetric subgroups on compact Lie groups to be biharmonic in terms of symmetric triad with multiplicities. By this criterion, we determine all the proper biharmonic submanifolds in irreducibl…
In this paper we obtain a sharp height estimate concerning compact hypersurfaces immersed into warped product spaces with some constant higher order mean curvature, and whose boundary is contained into a slice. We apply these results to draw topological conclusions at the end of the paper.
The abstract discusses compact quotients of Riemannian products by discrete subgroups, generalizing Inoue-Bombieri surfaces.
problem Compact quotients of Riemannian products by discrete subgroups.
method Study of compact quotients of a Riemannian product Rqimes(N,gN) by discrete subgroups Γ of Sim(Rq)imesIsom(N). result The construction is equivalent to LCP manifolds and provides a Bieberbach-type rigidity result.
Proves a Liouville-type theorem for p-Laplacian on manifolds.
problem Proving Liouville-type theorems for p-Laplacian on manifolds.
method Proved a Liouville-type result for the p-Laplacian on complete Riemannian manifolds.
result Proved a Liouville-type theorem for the p-Laplacian on complete non-compact Riemannian manifolds.
Study on astheno-Kähler structures on product manifolds.
problem Identifying astheno-Kähler structures on specific manifolds.
method Investigation of conditions on product of trans-Sasakian manifolds.
result Explicit constructions of astheno-Kähler manifolds.
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 …
We define generalized Atiyah-Patodi-Singer boundary conditions of product type for Dirac operators associated to C*-vector bundles on the product of a compact manifold with boundary and a closed manifold. We prove a product formula for the K-theoretic index classes, which we use to generalize the product formula for th…