arXiv research

Study adds scalar curvatures of mapped manifolds to Riemannian products.

The paper explores formulas and applications for mixed scalar curvature in multi-product manifolds.

Study on warped product Yamabe solitons with constant fiber curvature.

4D manifolds without positive scalar curvature but products do.

New rigidity found for 3D warped product domains.

New rigidity results for warped product domains.

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

Estimates mean curvature, scalar curvature, shape operator in warped products.

Proves curvature comparison for Riemannian bands in low dimensions.

New findings extend rigidity results to broader classes of manifolds.

Study compact sequences of warped product circles over spheres with nonnegative scalar curvature.

Study shows curvature rigidity of specific metric types.

We discuss conformal deformation and warped products on some open manifolds. We discuss how these can be applied to construct Riemannian metrics with specific scalar curvature functions.

Proves rigidity in product spaces using index theory.

The study extends Jacobi-orthogonality to indefinite scalar product spaces.

The paper explores conditions for positive scalar curvature on manifolds with boundaries and their doubles.

Characterizes warping functions in Einstein Poisson warped spaces.

Let $(M^m,g_M)$ be a closed, connected manifold with positive scalar curvature and $(T^k,g)$ some flat $k$-Torus of unit volume. By a result of F. Dobarro and E. Lami Dozo, there exists a unique $f: M \rightarrow \mathbf{R}_{>0}$ such that the warped product $M\times_f T^k$ has constant scalar curvature and unit volume…

The paper proves compactness of warped product metrics on S²×S¹ with varying base metrics.

Let $X$ be a compact connected Riemann surface of genus $g\geq 0$, and let ${\rm Sym}^d(X)$, $d \ge 1$, denote the $d$-fold symmetric product of $X$. We show that ${\rm Sym}^d(X)$ admits a Hermitian metric with negative Chern scalar curvature if and only if $g \geq 2$, and positive Chern scalar curvature if and only if…

Maps are shown to be Riemannian products with Ricci-flat fibers.

We consider the product of a compact Riemannian manifold without boundary and null scalar curvature with a compact Riemannian manifold with boundary, null scalar curvature and constant mean curvature on the boundary. We use bifurcation theory to prove the existence of a infinite number of conformal classes with at leas…

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

Paper studies convergence of nonnegative scalar curvature metrics to a specific limit space.

We consider the conformal class of the Riemannian product $g_0 + g$, where $g_0$ is the constant curvature metric on $S^m$ and $g$ is a metric of constant scalar curvature on some closed manifold. We show that the number of metrics of constant scalar curvature in the conformal class grows at least linearly with respect…

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…

We introduce the concept of a base conformal warped product of two pseudo-Riemannian manifolds. We also define a subclass of this structure called as a special base conformal warped product. After, we explicitly mention many of the relevant fields where metrics of these forms and also considerations about their curvatu…

In this paper, we study the Einstein multiply warped products with a semi-symmetric non-metric connection and the multiply warped products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connecti…

In this article we define the twisted product of groups as the generalization of the semidirect product of groups. We will find the necessary and sufficient condition in order that the twisted product of groups to be a group. In particular, for two copies of the same group, the twisted product of group by itself throug…

For a closed, connected direct product Riemannian manifold $(M, g)=(M_1\times\cdots\times M_l, g_1\oplus\cdots\oplus g_l)$, we define its multiconformal class $[\![ g ]\!]$ as the totality $\{f_1^2g_1\oplus \cdots\oplus f_l^2g_l\}$ of all Riemannian metrics obtained from multiplying the metric $g_i$ of each factor $M_…

Study relationships between intrinsic and extrinsic invariants of Riemannian almost k-product manifolds.

The study classifies quasi-Einstein manifolds with boundary.

Study torsion obstructions to positive scalar curvature on manifolds.

Let $M$ be either the 2-sphere $\SS^2 \subset\RR^3$ or the hyperbolic plane $\HH^2 \subset \RR^3$. If $Δ(abc)$ is a geodesic triangle on $M$ with corners at $a,b,c\in M$, we denote by $α, β, γ\in M$ the midpoints of their sides. If $Ω$ denotes the oriented area of this triangle on $M$, it satisfies the relations: $$ \s…

In this paper, we look for properties of gradient Yamabe solitons on top of warped product manifolds. Utilizing the maximum principle, we find lower bound estimates for both the potential function of the soliton and the scalar curvature of the warped product. By slightly modifying Li-Yau's technique so that we can hand…

The paper studies Einstein-Hilbert action on complex manifolds.

In this paper, we compute the index form of the multiply twisted products. We study the Killing vector fields on the multiply twisted product manifolds and determine the Killing vector fields in some cases. We compute the curvature of the multiply twisted products with a semi-symmetric metric connection and show that t…

It is known that the only finite-dimensional diffeological vector space that admits a diffeologically smooth scalar product is the standard space of appropriate dimension. In this note we consider a way to circumnavigate this issue, by introducing a notion of pseudo-metric, which, said informally, is the least-degenera…

We introduce partial secondary invariants associated to complete Riemannian metrics which have uniformly positive scalar curvature outside a prescribed subset on a spin manifold. These can be used to distinguish such Riemannian metrics up to concordance relative to the prescribed subset. We exhibit a general external p…

Paper proves convergence of warped product manifolds to a nonnegative scalar curvature limit.

In this paper, we provide a necessary and sufficient conditions for the warped product $M=B\times_f F$ to be a gradient Yamabe soliton when the base is conformal to an n-dimensional pseudo-Euclidean space, which are invariant under the action of an (n-1)-dimensional translation group, and the fiber F is scalar-constant…

In this paper we define a Poincaré-Reidemeister scalar product on the determinant line of the cohomology of any flat vector bundle over a closed orientable odd-dimensional manifold. It is a combinatorial "torsion-type" invariant which refines the PR-metric, introduced earlier by the first author, and contains an additi…

The study examines Einstein-Finsler spaces using Minkowskian products.

New method uses scalars to approximate physics functions.

We consider compact hypersurfaces in an $(n+1)$-dimensional either Riemannian or Lorentzian space $N^{n+1}$ endowed with a conformal Killing vector field. For such hypersurfaces, we establish an integral formula which, especially in the simpler case when $N=M^n\times R$ is a product space, allows us to derive some inte…

If the potential vector field of an $η$-Ricci soliton is of gradient type, using Bochner formula, we derive from the soliton equation a Laplacian equation satisfied by the potential function $f$. In a particular case of irrotational potential vector field we prove that the soliton is completely determined by $f$. We gi…

The abstract conjectures and proves conditions for scalar-flat Kähler surfaces with specific tensor properties.

New examples challenge Geroch conjecture stability.