arXiv research

The compact simply connected Riemannian 4-symmetric spaces were classified by J.A. Jim{é}nez. As homogeneous manifolds, these spaces are of the $G/H$, where $G$ is a connected compact simple Lie group with an automorphism $\tildeγ$ of oder 4 and $H$ is a fixed points subgroup $G^γ$ of $G$. In the present article, for t…

In this paper we give a geometrical interpretation of all the second elliptic integrable systems associated to 4-symmetric spaces. We first show that a 4-symmetric space $G/G_0$ can be embedded into the twistor space of the corresponding symmetric space $G/H$. Then we prove that the second elliptic system is equivalent…

Let G/H be a compact 4-symmetric space of inner type such that the dimension of the center Z(H) of H is at most one. In this paper we shall classify involutions of G preserving H for the case where dim Z(H)=0, or H is a centralizer of a toral subgroup of G.

Study automorphisms and subgroups of exceptional Lie group E8.

New pseudo-Kähler Einstein spaces found with special almost complex structures.

Completed realizations of automorphisms and subgroups in exceptional Lie group $E_8$.

An order four automorphism of a Lie algebra gives rise to an integrable system discussed by Terng. We show that solutions of this system may be identified with certain vertically harmonic twistor lifts of conformal maps of surfaces in a Riemannian symmetric space. Specialising to 4-dimensional target, we find that surf…

We study supersymmetric harmonic maps from the point of view of integrable system. It is well known that harmonic maps from R^2 into a symmetric space are solutions of a integrable system . We show here that the superharmonic maps from R^{2|2} into a symmetric space are solutions of a integrable system, more precisely …

In this work we study the existence of homogeneous Einstein metrics on the total space of homogeneous fibrations such that the fibers are totally geodesic manifolds. We obtain the Ricci curvature of an invariant metric with totally geodesic fibers and some necessary conditions for such a metric to be Einstein in terms …

After a self-contained introduction to Lie algebra cohomology, we present some recent applications in mathematics and in physics. Contents: 1. Preliminaries: L_X, i_X, d 2. Elementary differential geometry on Lie groups 3. Lie algebra cohomology: a brief introduction 4. Symmetric polynomials and higher order cocycles 5…

The paper identifies special Lagrangian shapes in 4D space.

Dynamics of four-dimensional massless fields of all spins is formulated in the Siegel space of complex $4\times 4$ symmetric matrices. It is shown that the unfolded equations of free massless fields, that have a form of multidimensional Schrodinger equations, naturally distinguish between positive- and negative-frequen…

It is known that complex constant mean curvature ({\sc CMC} for short) immersions in $\mathbb C^3$ are natural complexifications of {\sc CMC}-immersions in $\mathbb R^3$. In this paper, conversely we consider {\it real form surfaces} of a complex {\sc CMC}-immersion, which are defined from real forms of the twisted $\m…

Study confirms conjectures on Ricci limit spaces and their topological properties.

Elliptic curve governs Hopf linking in symmetric tensegrity.

The paper establishes new Casorati inequalities for various Riemannian maps and submersions.

Survey on gluing constructions under lower curvature bounds.

Study on Riemannian Poisson warped product spaces and their properties.

Paper studies quaternionic space forms and Riemannian maps inequalities.

Rigidity of Wasserstein spaces over Riemannian manifolds

Introduces a new framework for Riemannian diffeology.

Develops calculus on Wasserstein spaces for Riemannian manifolds.

We prove that Berwald spaces whose flag curvature is nowhere vanishing are in fact Riemannian spaces. This means that any Berwald space with flag curvature bounded below by a positive number must be also Riemannian. This rigidity result shows the importance of non-Riemannian examples when imposing flag curvature bounds…

Paper defines minimal hypersurfaces in Euclidean and Riemannian spaces.

Unified study of Riemannian and sub-Riemannian geometries with synthetic Ricci curvature bounds.

Minimal polynomial found for Riemannian C_0-spaces.

Establish generalized Chen inequalities for Riemannian submersions and Riemannian maps with applications.

In this paper, we derived biharmonic equations for pseudo-Riemannian submanifolds of pseudo-Riemannian manifolds which includes the biharmonic equations for submanifolds of Riemannian manifolds as a special case. As applications, we proved that a pseudo-umbilical biharmonic pseudo-Riemannian submanifold of a pseudo-Rie…

We classify pseudo-Riemannian submersions with connected totally geodesic fibres from a real pseudo-hyperbolic space onto a pseudo-Riemannian manifold. Also, we obtain the classification of the pseudo-Riemannian submersions with (para-)complex connected totally geodesic fibres from a (para-)complex pseudo-hyperbolic sp…

The leaf space of a Killing Riemannian foliation is a diffeological quasifold.

Riemannian manifolds of quasi-constant sectional curvatures (QC-manifolds) are divided into two basic classes: with positive or negative horizontal sectional curvatures. We prove that the Riemannian QC-manifolds with positive horizontal sectional curvatures are locally equivalent to canal hypersurfaces in Euclidean spa…

We classify the semi-Riemannian submersions from a pseudo-hyperbolic space onto a Riemannian manifold under the assumption that the fibres are connected and totally geodesic. Also we obtain the classification of the semi-Riemannian submersions from a complex pseudo-hyperbolic space onto a Riemannian manifold under the …

The paper proves unique properties of Riemannian twistor spaces under specific curvature conditions.

Study shows discrete spectra on base spaces for certain Riemannian submersions.

The paper classifies submanifolds in pseudo-Riemannian space forms.

New submersion proves complex-valued harmonic map existence.

The study classifies quasi-minimal surfaces in 4D pseudo-Riemannian space-forms with positive nullity.

Paper derives sub-Riemannian versions of Kastler-Kalau-Walze and Dabrowski-Sitarz-Zalecki theorems for twisted BCV spaces.

The paper examines curvature properties of twistor spaces.

Study on sets with positive reach in Euclidean and Riemannian spaces.

We prove the integrability of geodesic flows on the Riemannian g.o. spaces of compact Lie groups, as well as on a related class of Riemannian homogeneous spaces having an additional principal bundle structure.

The paper studies Finsler spaces with semi-concurrent vector fields and their equivalence to Riemannian spaces.

Study Riemannian metrics on lens spaces, find cut loci and diameters.

Study Riemannian metrics on lens spaces, find cut loci and diameters.

Survey on smooth function and form density in Riemannian Sobolev spaces.

The paper derives inequalities for Riemannian submersions and their applications.

The paper derives inequalities for Riemannian maps and submersions involving quaternionic space forms.

The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from the Satake diagram, in a way that is suited for the use with comput…