arXiv research

Study spherical T-duality and Massey products in iterated sphere bundles.

Spherical T-duality for iterated sphere bundles

Classifies smooth manifolds homotopy equivalent to sphere products

The purpose of this paper is to give an effective construction for some induced structures on spheres or product of spheres of codimension 1, 2 or 3, respectively, in Euclidean space endowed with an almost product structure.

We discuss the integrability of orthogonal almost complex structures on Riemannian products of even-dimensional round spheres and give a partial answer to the question raised by E. Calabi concerning the existence of complex structures on a product manifold of a round 2-sphere and a round 4-sphere.

Study approximates product of spheres using Laplacian eigenvalues.

The study classifies parallel mean curvature spheres in a sphere-hyperbolic product space.

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…

We show that essential punctured spheres in the complement of links with distance three bridge spheres have bounded complexity. We define the operation of tangle product, a generalization of both connected sum and Conway product. Finally, we use the bounded complexity of essential punctured spheres to show that the bri…

Existence proved for Ricci curvature on sphere product.

The present paper discusses that a prescribed Gauss-Kronecker curvature problem on the product of unit spheres.

The study finds compact vacuum static spaces with positive isotropic curvature are spheres or products of a circle and sphere.

Functional determinant for mixed signature sphere products depends on sphere dimensions and parity.

The aim of this paper is to write an explicit orthonormal parallelization for all parallelizable products of spheres, using an explicit isomorphism with a trivial vector bundle.

We use the notion of fixity for representations of finite groups to construct free and smooth actions on products of spheres. In particular we show that a finite p-group (for p>3) will act freely and smoothly on a product of two spheres if and only if it does not contain a rank 3 elementary abelian subgroup. We show th…

A well known conjecture in the theory of transformation groups states that if p is a prime and (Z/p)^r acts freely on a product of k spheres, then r is less than or equal to k. We prove this assertion if p is large compared to the dimension of the product of spheres. The argument builds on tame homotopy theory for non …

We show that various classes of products of manifolds do not support transitive Anosov diffeomorphisms. Exploiting the Ruelle-Sullivan cohomology class, we prove that the product of a negatively curved manifold with a rational homology sphere does not support transitive Anosov diffeomorphisms. We extend this result to …

Our aim in this paper is to give some examples of $(a, 1)f$ Riemannian structures (a generalization of an $r$-paracontact structure) induced on product of spheres of codimension $r$ ($r \in \{1,2\}$) in an $m$-dimensional Euclidean space ($m>2$), endowed with an almost product structure.

Study degenerate solutions on product of spheres using bifurcation theory.

Minimal submanifolds in spheres can be produced via Clifford type minimal products, and their Morse indices and nullities are calculated.

Abstract: Study gyrations of sphere products and connected sums, generalizing Fico's Lemmata.

We give explicit formulas for the intertwinors on the scalar functions over the product of spheres with the natural pseudo-Riemannian product metric using the spectrum generating technique. As a consequence, this provides another proof of the even order conformally invariant differential operator formulas obtained earl…

Study proves Łojasiewicz inequalities for self-shrinkers, aiding in their uniqueness.

The article provides formulas for the number of terms in connected sums of sphere products associated with dual-neighborly polytopes.

We give a complete enumeration of all combinatorial 3-manifolds with 10 vertices: There are precisely 247882 triangulated 3-spheres with 10 vertices as well as 518 vertex-minimal triangulations of the sphere product $S^2\times S^1$ and 615 triangulations of the twisted sphere product $S^2_\times_S^1$. All the 3-spheres…

This study shows the moment-SOS hierarchy converges in polynomial optimization over product of spheres.

We study CR geometry in arbitrary codimension, and introduce a process, which we call the Levi-Kahler quotient, for constructing Kahler metrics from CR structures with a transverse torus action. Most of the paper is devoted to the study of Levi-Kahler quotients of toric CR manifolds, and in particular, products of odd …

Study shows curvature rigidity of specific metric types.

Identifies a mod-$p$ triple cup product for rational homology 3-spheres with specific first homology.

Being E a vector space with inner product and S the sphere of E, will be given a demonstration that every application of the sphere S itself it such that preserve inner product is the restriction of a linear isometry in E.

The study examines hypersurfaces in warped products and their properties.

The paper proves rigidity for warped product spaces with degenerate ends.

We define invariants $\frak{ds}$ and $\overline{\frak{ds}}$, which are the maximal and minimal second Betti number divided by $8$ among definite spin boundings of a homology sphere. The similar invariants $g_8$ and $\overline{g_8}$ are defined by the maximal (or minimal) product sum of $E_8$-form of bounding 4-manifold…

Sharp bounds for eigenfunctions on product spaces restricted to submanifolds.

We construct an unbounded representative for the shriek class associated to the embeddings of spheres into Euclidean space. We equip this unbounded Kasparov cycle with a connection and compute the unbounded Kasparov product with the Dirac operator on $\mathbb R^{n+1}$. We find that the resulting spectral triple for the…

The paper classifies smooth structures on product manifolds of 3-connected 8-manifolds with spheres.

Paper proves no stable Yang-Mills fields on spheres.

Durhuus and Jonsson (1995) introduced the class of "locally constructible" (LC) triangulated manifolds and showed that all the LC 2- and 3-manifolds are spheres. We show here that for each d>3 some LC d-manifolds are not spheres. We prove this result by studying how to collapse products of manifolds with exactly one fa…

The volume spectrum of fiber bundles is bounded by the product of the base's volume spectrum and the fiber's volume.

We describe, under some additional technical assumptions, the Gromov boundary of the free product of several $G_i$'s amalgamated wrt. $H$, where $G_i$ are hyperbolic groups with boundary homeomorphic to a densely punctured $n$-sphere, and $H$ is their common subgroup corresponding to a peripheral sphere in each of the …

In this paper, we obtain a sufficient and necessary condition for a simply connected Riemannian manifold $(M^n, g)$ to be isometrically immersed, as a submanifold with codimension $p\geq 1$, into the product $S^k\times H^{n+p-k}$ of sphere and hyperboloid.

The study compares and finds Yamabe constants on warped products.

In this paper we construct Ricci-positive metrics on the connected sum of products of arbitrarily many spheres provided the dimensions of all but one sphere in each summand are at least 3. There are two new technical theorems required to extend previous results on sums of products of two spheres. The first theorem is a…

Harmonic unit normal sections studied for Grassmannians induced by cross products.

The study examines minimal surfaces in Riemannian products of surfaces.

We prove a Reeb sphere theorem for finite simple graphs. The result bridges two different definitions of spheres in graph theory. We also reformulate Morse conditions in terms of the center manifolds, the level surface graphs {f=f(x)} in the unit sphere S(x). In the Morse case these graphs are either spheres, the empty…

Study shows magnetic trajectories in Berger spheres are homogeneous.

Paper constructs new minimal submanifolds in spheres by spinning given ones.