arXiv research

Generalizes symmetries of curved manifolds.

The study characterizes symmetries in Kaehler manifolds.

Symmetries of Einstein-Weyl manifolds can be extended from boundary surfaces.

A condition for a statistical manifold to have an equiaffine structure is studied. The facts that dual flatness and conjugate symmetry of a statistical manifold are sufficient conditions for a statistical manifold to have an equiaffine structure were obtained in [2] and [3]. In this paper, a fact that a statistical man…

Study on Frobenius manifold structures and inversion symmetry.

The study of symmetries in manifolds derived from colored polytopes.

The symmetry-rank of a riemannian manifold is by definition the rank of its isometry group. We determine precisely which smooth closed manifolds admit a positively curved metric with maximal symmetry-rank.

The study examines symmetries in spaces with positive or non-negative curvature.

Researchers discover symmetries in Ricci flows and use them to find invariant solutions.

Study proves Hodge symmetry on Oeljeklaus-Toma manifolds with line bundles.

We study dg-manifolds which are R[2]-bundles over R[1]-bundles over manifolds, we calculate its symmetries, its derived symmetries and we introduce the concept of T-dual dg-manifolds. Within this framework we construct the T-duality map as a degree -1 map between the cohomologies of the T-dual dg-manifolds and we show …

We generalize the symmetry superalgebras of isometries and geometric Killing spinors on a manifold to include all the hidden symmetries of the manifold generated by Killing spinors in all dimensions. We show that bilinears of geometric Killing spinors produce special Killing-Yano and special conformal Killing-Yano form…

We establish a vanishing result for indices of certain twisted Dirac operators on $\text{Spin}^c$-manifolds with non-abelian Lie-group actions. We apply this result to study non-abelian symmetries of quasitoric manifolds. We give upper bounds for the degree of symmetry of these manifolds.

Curved 10-manifolds with torus symmetry are spheres or complex projective spaces.

Invariants found for tau-symmetric bihamiltonian systems.

Extended Einstein manifolds reveal new symmetries.

Local normal forms for symmetrical contact structures on 3-manifolds.

Study $G_2$ manifolds with symmetry, finding new submanifolds.

In this paper, we give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain four dimensional fiber bundles by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau. As a corollary of this estimate, we compute the degree of symmetry and the semi-simple degree o…

Symmetries of Poisson manifolds are in general quantized just to symmetries up to homotopy of the quantized algebra of functions. It is therefore interesting to study symmetries up to homotopy of Poisson manifolds. We notice that they are equivalent to Poisson principal bundles and describe their quantization to symmet…

A "hidden symmetry" of a Riemannian manifold M is an isometry of a d-sheeted, 1<d<\infty, Riemannian cover of M which is not the lift of any isometry. In this paper we characterize the locally symmetric metric(s) on a closed, arithmetic manifold as the unique metric with infinitely many hidden symmetries.

Every compact aspherical Riemannian manifold admits a canonical series of orbibundle structures with infrasolv fibers which is called its infrasolv tower. The tower arises from the solvable radicals of isometry group actions on the universal covers. Its length and the geometry of its base measure the degree of continuo…

Linearizes Virasoro symmetries for semisimple Frobenius manifolds.

Geometric quantization shows compatibility of symmetries on coadjoint orbits and Kähler-Einstein manifolds.

We introduce a geometric invariant that we call the index of symmetry, which measures how far is a Riemannian manifold from being a symmetric space. We compute, in a geometric way, the index of symmetry of compact naturally reductive spaces. In this case, the so-called leaf of symmetry turns out to be of the group type…

New rigidity results for manifolds with maximal symmetry rank and positive intermediate Ricci curvature.

Locally homogeneous Lorentzian three-manifolds with recurrect curvature are special examples of Walker manifolds, that is, they admit a parallel null vector field. We obtain a full classification of the symmetries of these spaces, with particular regard to symmetries related to their curvature: Ricci and matter colline…

New method discovers symmetries in differential equations from data.

The paper simplifies symmetries in complex geometric structures.

Extended symmetries and anomalies in compactified 6d SCFTs on various internal manifolds.

Study on symmetries of quaternionic Kähler manifolds with S^1-symmetry.

We show that the indices of certain twisted Dirac operators vanish on a $Spin$-manifold $M$ of positive sectional curvature if the symmetry rank of $M$ is $\geq 2$ or if the symmetry rank is one and $M$ is two connected. We also give examples of simply connected manifolds of positive Ricci curvature which do not admit …

We study the index of symmetry of a compact generalized flag manifold M=G/H endowed with an invariant Kaehler structure. When the group G is simple we show that the leaves of symmetry are irreducible Hermitian symmetric spaces and we estimate their dimension.

Study on special symmetries in biwarped product 3-manifolds.

We introduce self-dual manifolds and show that they can be used to encode mirror symmetry for affine-Kähler manifolds and for elliptic curves. Their geometric properties, especially the link with special lagrangian fibrations and the existence of a transformation similar to the Fourier-Mukai functor, suggest that this …

The paper explores symmetries in Kähler manifolds using Ricci tensor properties.

We classify closed, simply-connected, non-negatively curved 6-manifolds of almost maximal symmetry rank up to equivariant diffeomorphism.

On locally conformally flat manifolds we describe a construction which maps generalised conformal Killing tensors to differential operators which may act on any conformally weighted tensor bundle; the operators in the range have the property that they are symmetries of any natural conformally invariant differential ope…

The paper explores symmetry in solutions of semilinear PDEs on Riemannian domains.

Researchers compute c-projective symmetry algebras for Kähler surfaces.

Classifies maximal symmetry models of CR dimension 1.

Constructs integrable hierarchies for generalized Frobenius manifolds with non-flat unity.

Defines discrete symmetry of manifolds and proves bounds on its value.

The study explores Hesse manifolds and their symmetries in multifield cosmological models.

We use a local argument to prove if an $r$-dimensional torus acts isometrically and effectively on a connected $n$-dimensional manifold which has positive $k^\mathrm{th}$-intermediate Ricci curvature at some point, then $r \leq \lfloor \frac{n+k}{2} \rfloor$. This symmetry rank bound generalizes those established by Gr…

We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group A_n which is not the topological symmetry group of any graph embedded in the manifold. We also show that for every finite group G, there is an embedding Γ of some graph in a hyperbolic rational homology 3-sp…

We prove a Bishop volume comparison theorem and a Laplacian comparison theorem for three dimensional contact subriemannian manifolds with symmetry.

We address the issue why Calabi-Yau manifolds exist with a mirror pair. We observe that the irreducible spinor representation of the Lorentz group Spin(6) requires us to consider the vector spaces of two-forms and four-forms on an equal footing. The doubling of the two-form vector space due to the Hodge duality doubles…